beginequationbeginarrayltext-a-53125-text-so-log-text-b-log-_5-252-text-so-endarrayendequation

Question

\begin{equation}\begin{array}{l}{	ext { (a) } 5^{3}=125, 	ext { so log }} \ {	ext { (b) } \log _{5} 25=2, 	ext { so }}\end{array}\end{equation}

Erna Bisschoff · Accepted Answer

backing this question. We have to change a into the loch form Nagar ethnic form and be back into exponential form in order to do that, let&#x27;s start off the definition off the lock, the relationship off lock and exponential form. So if we have any lock to base off a be equal to X right. So let&#x27;s see how it all fits together. The eye is the base off the log. So it becomes the base off the exponential form. Right? So you can dream, baby, this one to base, always a base. So the base off the lock becomes the base off the exponential form. Then the eggs is the exponents, so we have the base to the exponents on. Then we have the be left on the other side. Right? So it&#x27;s also this thing for a We have five as the base off the exponential form so we can put that in as the base off the lock. Then the experiment is three. So that will be on the other side. And we have the 125 inside the lock. Right. It&#x27;s good to be for B. We have to stop the ground. We have five as the base, the two as the exponents and in 25 on the other side off the equation.

Jocelyn Shackelford · Answer

in order to solve the equation. 25 raised to the X Plus three is equal to five. Raise toe X plus four. First, we have to log both sides by logging both sides. We can bring these exponents to the front. This is one of the rules of longer thems. After this, we will divide both sides by log. Five Long 25 divided by five is equal to two, which we will set equal to X minus four. After this, all we have to do is sell for X so two X plus six it is equal to X minus four. Add four to both sides. Subtract two x from both sides and you find that the answer is negative. 10 equals X.

Elizabeth Xu · Answer

so to solve for X in this equation, when we first need to do is make everything have a base of five. So the left side We know that with properties of exponents you multiply two exponents who are two numbers with the same base. You know the exponents will be a five to the six sects. Does he go to five to the third power? So six axes Eagle three and X is equal to 1/2.

Amy Jiang · Answer

Okay, So on our left inside, we can use our product roasted at steep US forward at six. And then 125. That&#x27;s 52 or three. Now, by our uniqueness property, we know that six X is equal to three, which means that X must be equal to 1/2.

Heather Zimmers · Answer

to solve this equation. I&#x27;m going to start by combining these two factors. We know that we can add the exponents when we have the same base. So we would have five to the six. X Power equals 1 25 and we can also rewrite 1 25 as a power of five. It&#x27;s with five to the six. X power equals five to the third power. And because of that, we can set the exponents equal to each other. So six x equals three and dividing by six we get X equals 1/2.

Sarah Stryke · Answer

All right, We&#x27;re on question 2 98 and were asked to solve for X O says 625 times five to the three x plus trees equal to 1.5. Thinking about the properties we use on the previous problems, we want to be able to simplify this. I could potentially divide both sides by 6 25 But I think I&#x27;m gonna be able to break this down to 52 in exploded. And if I&#x27;m able to do that, then I can use this rule over here. A to the end, times a to the n is equal to a to the end. Plus, in a song with my faces are the same, I would be able to multiply. The exponents are multiplied factors together and add the exponents. So let&#x27;s give that a try. Um, let&#x27;s use prime factory ization to break down our 6 25 so I can clearly see that 6 25 is divisible by five. So that is helpful. So let&#x27;s start with lies. Times 100 in 25 Pray five is a prime shell. Let&#x27;s leave that And 11 25 is going to be five times 25. And lastly, we have 25 is five times spots. So what this means is I can actually rewrite 5 25 as five to the fourth power. So five to the fourth power times five three X plus three. Is he a little one? 25. Okay, now that our were multiplying and our bases are the same, we could go ahead and add these explosives together. So to go ahead and get five. What? Plus the re exposed three is equal to one 25. Great simple violas. Five to the three x. 07 is equal to 1 25 Now, in order for us to be the 1 to 1 property again, these bases have to be the same. So et the extra cold aid the Why then I can set x equal if I so see if we can break down our 1 25 So 1 25 5 25 not spy appendicitis. So 1 25 is actually five to the third power so far to the third power. Greek will too. Come on. So the three x course seven. All right, so now that we have the same basis. We could set our exponents equal to each other. So let&#x27;s make this the ex Lost seven is equal to three, and we will solve for X. So it&#x27;s a tractor seven from both sides. That&#x27;s three eggs is equal to negative for in the last legal divide, both sides three Idol answer would be X is equal to negative for words, and we complain that back into our original function to double check and make sure that it&#x27;s correct.

Problem

Match the logarithmic function with its graph. \…

Problem 3 Easy Difficulty

\begin{equation}\begin{array}{l}{\text { (a) } 5^{3}=125, \text { so log }} \\ {\text { (b) } \log _{5} 25=2, \text { so }}\end{array}\end{equation}

Answer

$$
\begin{array}{l}{\text { (a) } \log _{5} 125=3} \\ {\text { (b) } 5^{2}=25}\end{array}
$$

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$$\begin{array}{l}{\text { (a) } \log _{5} 125=3} \\ {\text { (b) } 5^{2}=25}\end{array}$$

Algebra and Trigonometry

Grace H.

Kayleah T.

Maria G.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

James Stewart, Lothar Redlin, Saleem WatsonAlgebra and Trigonometry

Grace H.

Kayleah T.

Maria G.

Michael J.

$$
\begin{array}{l}{\text { (a) } \log _{5} 125=3} \\ {\text { (b) } 5^{2}=25}\end{array}
$$

James Stewart, Lothar Redlin, Saleem Watson

Algebra and Trigonometry