# Solve for x to the nearest hundredth. 3^x = 1.295

## Question:

Solve for {eq}x {/eq} to the nearest hundredth.

{eq}3^x = 1.295 {/eq}

## Solving for a variable

We have to solve the given equation for **x**. However, **x** is an exponent and, as the base on both sides of the equation can not be made, the only way of bringing it down is by using the natural log.

## Answer and Explanation:

The equation is solved as follows by taking the natural log of both sides.

$$\begin{align} 3^x& = 1.295\\ x\ln 3&=\ln 1.295&&&&\text{Taking the natural log of both the sides}\\ x&=\frac{\ln 1.295}{\ln 3}\\ \therefore x&=0.2353 \end{align} $$

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