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

Answer:

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

Step-by-step 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, $56=x^8\\\\\\56^{\frac{1}{8}}=x^{(8\times{\frac{1}{8}})$

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