Question

Margee thinks she can use logs to solve 56 = x^8, since logs seem to make exponents disappear. Unfortunately, Margee is wrong. Explain the difference between equations like 2 = 1.04^x, in which you can use logs, and 56 = x^8, in which it does not make sense to use logs.

Answer 1

We use log to solve only those equations in which we have our variables in power form.

Explanation:

Given : Margee thinks she can use logs to solve
`56=x^8`, since logs seem to make exponents disappear but Margee is wrong

We have to explain the difference between equations like
`2=(1.04)^x` and
`56=x^8`

We use log to solve only those equations in which we have our variables in power form.

Out of given equation only
`2=(1.04)^x` has x in power form so we can apply log for solving the equation as,

`2=(1.04)^x\\\\\ \text{Taking ln both sides},\\\ln (2)=\ln (1.04)^x\\\\\\\\text{Using idenity} \ln a^b=b\ln a\\\\\\ln (2)=\ln (1.04)^x\\\\\text{on solving, we get}\\\\x=17.673`

While solving other equation ,

`56=x^8`, we can directly take 8 root both side,
`56=x^8\\\\\\56^{(1)/(8)}=x^{(8*{(1)/(8)})`

Thus, We use log to solve only those equations in which we have our variables in power form.