Question

Given the exponential equation 3* = 243, what is the logarithmic form of the equation in base 10? (5 points)

Answer 1

Answer:

$x = \frac{log\ 243}{log\ 3}$

Step-by-step explanation:

Given

$3^x = 243$

Required

Express as a logarithm

$3^x = 243$

Take log of both sides

$log\ 3^x = log\ 243$

Apply the following law of logarithm

$log\ a^b = b\ log\ a$

So, the expression becomes:

$log\ 3^x = log\ 243$

$x\ log\ 3 = log\ 243$

Divide both sides by log 3

$\frac{x\ log\ 3}{log\ 3} = \frac{log\ 243}{log\ 3}$

$x = \frac{log\ 243}{log\ 3}$

Hence, the expression in base 10 is:

$x = \frac{log\ 243}{log\ 3}$ or $x = \frac{log_{10}\ 243}{log_{10}\ 3}$