Convert the exponential equations into logarithmic form: (a)...

Convert the exponential equations into logarithmic form: (a) $2^3 = 8$ is equivalent to $log_2 C = D$. C = and D = (b) $16 = 4^2$ is equivalent to $log_4 E = F$. E = and F = (c) $10^4 = 10000$ is equivalent to $log_{10} G = H$. G = and H = (d) $0.001 = 10^{-3}$ is equivalent to $log_{10} J = K$. J = and K =

Transcript

00:01 In the given question we are told to convert the following exponential equations to logarithmic form.

00:06 So the first equation that is given to us is 2 raised to the power 5 is equal to 32 and we should write it in the form of long with base 2 of c is equal to d.

00:22 And what we have to find over here is the value of c and d.

00:27 So what we can do is first let's write a property, a logarithmic property, that is when we have log with base a of a to the power b, it is equal to b.

00:40 So this is a property that we can use over here.

00:46 So now what we can do is when we take log with base a of 2 to the log with base a of 2 to the log with base 2 of 2 to the power 5 which is equal to the power of 2 over here which is 5 right so according to this property log with base a of a to the power b is equal to the power of a which over here is b and over here it is equal to 5 so 2 to the power 5 is what it is 32 right so instead of 2 to the power of 5 we can write 32 over here and this would be the required logarithmic equation.

01:32 So we can write c over here is equal to 32 and d is equal to 5.

01:38 So this is the answer for the first part of this question.

01:43 Now let's move on to the second exponential equation which is given as 36 is equal to 6 squared.

01:51 So over here this would be of the form log with base 6.

01:56 Of e is equal to f so we can write just as we have done before log with base 6 of 6 squared is equal to 2 which is the base of 6 over here so then the equation would be log with base 6 of 36 which is 6 squared is equal to 2 from here we can write e is then equal to 36 and f is equal to 2 so now moving on to the next exponential equation equation we have 10 to the power 4 is equal to 10 ,000 and we have to write an equivalent exponential equation which is log with base 10 of g is equal to h so we can write log with base 10 of 10 to the power 4 is equal to 4 and now instead of 10 to the power 4 we we can write log with base 10 of 10 ,000 is equal to 4...

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