Question

Solve each equation for x. If your answer is a decimal, round to the nearest hundredth.

Answer 1

Given the equation below

`\log_x27=-3`

To find the value of x, we apply logarithms rule

`Multiply\text{ both sides by }\log_(27)x`

Crosssmultiply

`\begin{gathered} \log_(27)x*\log_x27=-3\log_(27)x \\ 1=-3\log_(27)x \end{gathered}`

Divide both sides by -3

`\begin{gathered} -(1)/(3)=\log_(27)x \\ Simplifying\text{ the above expression } \\ x=(1)/(3) \end{gathered}`

Hence,

`x=(1)/(3)`