Question

Solve the logarithmic equation. Round your answers to the nearest hundredth. 6+in x=8

Answer 1

well, assuming is not inches, and instead is ln(x).


`\bf \textit{Logarithm Cancellation Rules}\\\\ log_a a^x= x\qquad \qquad \boxed{a^(log_ax)=x}\\\\ -------------------------------\\\\ 6+ln(x)=8\implies ln(x)=2\implies log_e(x)=2 \\\\\\ e^(log_e(x))=e^2\implies x=e^2`

Answer 2

`x=7.39`

Explanation:

we are given equation as

`6+ln(x)=8`

Since, we have to solve for x

so, we will isolate x on anyone side

Firstly, we will subtract both sides by 6

`6+ln(x)-6=8-6`

`ln(x)=2`

now, we can take exponent of e on both sides

`e^(ln(x))=e^2`

now, we can use property of log

and we get

`e^(ln(a))=a`

we can use it

`x=e^2`

So, solution is

`x=7.39`