Question

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

Answer 1

Solution

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

$\begin{gathered} \log_{27}x\times\log_x27=-3\log_{27}x \\ 1=-3\log_{27}x \end{gathered}$

Divide both sides by -3

$\begin{gathered} -\frac{1}{3}=\log_{27}x \\ Simplifying\text{ the above expression } \\ x=\frac{1}{3} \end{gathered}$

Hence,

$x=\frac{1}{3}$