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.

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