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\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}

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

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Harvey Mudd College

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

02:15

Solve: $25^{x+3}=5^{x-4}.$…

00:29

Solve each equation.$$…

00:15

00:33

solve each equation.$5…

05:23

Use like bases to solve th…

05:29

$$\begin{aligned}&\lef…

04:05

Solve.$\frac{x}{x-5}+\…

01:29

Solve$x^{3}+5 x^{2}-25…

04:32

Simplify.$$\frac{1…

00:22

$$\left(\frac{2}{5}\right)…

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'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'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'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'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.

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In mathematics, the absolute value or modulus |x| of a real number x is its …

Solve: $25^{x+3}=5^{x-4}.$

Solve each equation.$$5^{2 x} \cdot 5^{4 x}=125$$

solve each equation.$5^{2 x} \cdot 5^{4 x}=125$

Use like bases to solve the exponential equation.$625 \cdot 5^{3 x+3}=12…

$$\begin{aligned}&\left(\begin{array}{l}5 \\0\end{array}\right)\left(\fr…

Solve.$\frac{x}{x-5}+\frac{5}{x+5}=-\frac{1}{x^{2}-25}$

Solve$x^{3}+5 x^{2}-25 x \leq 125$

Simplify.$$\frac{125^{-4}\left(25^{2}\right)^{4}}{125}$$

$$\left(\frac{2}{5}\right)^{-2}$$

06:00

Graphing Rational Functions Find the intercepts and asymptotes, and then ske…

$91-92=$ Graphing Even and Odd Functions The graph of a function defined for…

01:06

$9-22$ Evaluating Logarithms Use the Laws of Logarithms toevaluate the e…

00:45

23-48 Expanding Logarithmic Expressions Use the Laws ofLogarithms to exp…

04:43

Match the logarithmic function with its graph.\begin{equation}\begin{arr…

01:33

We can expand $\log \left(\frac{x^{2} y}{z}\right)$ to get _________________…

03:26

$71-74=$ Graphing Transformations The graph of a function $f$ is given. Sket…

01:50

$47-64=$ Finding Complex Zeros Find all zeros of thepolynomial.

…

$37-46=$ Finding a Polynomial with Specified Zeros Find apolynomial with…

00:35

Finding Values of an Inverse Function Assume that $f$ isa one-to-one fun…

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