# How do you solve 3^(2x) = 75?

$x = 1.9649735207179$

#### Explanation:

Start from the given equation:

${3}^{2 x} = 75$

Take the logarithm of both sides of the equation

${\log}_{10} {3}^{2 x} = {\log}_{10} 75$

$\left(2 x\right) \cdot {\log}_{10} 3 = {\log}_{10} 75$

divide both sides of the equation by ${\log}_{10} 3$

$\frac{\left(2 x\right) \cdot {\log}_{10} 3}{\log} _ 10 3 = {\log}_{10} \frac{75}{\log} _ 10 3$

$\frac{\left(2 x\right) \cdot \cancel{{\log}_{10} 3}}{\cancel{{\log}_{10} 3}} = {\log}_{10} \frac{75}{\log} _ 10 3$

$2 x = {\log}_{10} \frac{75}{\log} _ 10 3$

$x = \frac{1}{2} \cdot {\log}_{10} \frac{75}{\log} _ 10 3$ the exact value

color (red)(x=1.9649735207179 the calculator value

Check: at $x = 1.9649735207179$

${3}^{2 x} = 75$

${3}^{\left(2 \cdot \left(1.9649735207179\right)\right)} = 75$

$75 = 75$

Have a nice day !!! from the Philippines...