# How do you calculate log_7 8.34 with a calculator?

Aug 23, 2016

${\log}_{7} 8.34 \cong 1.09001$

#### Explanation:

Using the relationship:
${\log}_{b} x = {\log}_{a} \frac{x}{\log} _ a b$

In this example $x = 8.34 \mathmr{and} b = 7$
and let $a = 10$ (to allow the calculation on a simple scientific calculator.)

Hence: ${\log}_{7} 8.34 = {\log}_{10} \frac{8.34}{\log} _ 10 7$

$\cong \frac{0.92117}{0.84510}$

$\cong 1.09001$

NB: To check result ${7}^{1.09001} = 8.34$ to 2 decimals