# How do you solve 4^(2x+3)=1?

Aug 27, 2016

$x = - \frac{3}{2}$

#### Explanation:

Properties of logarithms
$y = {\log}_{a} x$ is the same as ${a}^{y} = x$

Your posted equation will be $2 x + 3 = {\log}_{4} 1$

To solve the right side, if you don't have a calculator that with a change of base: Enter $L O G \left(1\right)$/LOG(4) into your calculator to get the correct answer. You divide the log by the number you want to change the base to.

That gives you 2x+3=0. From there it's simple algebra. Subtract the 3 from each side and divide both sides by 2. Leaving you with $x = - \frac{3}{2}$ .

Always check your answers. 4^(2*(-3/2)+3 = 1