Question

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

log, 243

log, 3

log, 3

log, 243

log,03

log, 243

log, 243

Answer 1

`x = (log\ 243)/(log\ 3)`

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

`(x\ log\ 3)/(log\ 3) = (log\ 243)/(log\ 3)`

`x = (log\ 243)/(log\ 3)`

Hence, the expression in base 10 is:

`x = (log\ 243)/(log\ 3)` or
`x = (log_(10)\ 243)/(log_(10)\ 3)`