How do you calculate ${log}_{7} 8.34$ $log_7 8.34$ with a calculator?

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Answer 1 · 2016-08-23T03:21:42

${log}_{7} 8.34 ≅ 1.09001$ $log_7 8.34~=1.09001$

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

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

Hence: ${log}_{7} 8.34 = \frac{{log}_{10} 8.34}{{log}_{10} 7}$ $log_7 8.34 = log_10 8.34/log_10 7$

$≅ \frac{0.92117}{0.84510}$ $~= 0.92117/0.84510$

$≅ 1.09001$ $~= 1.09001$

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

How do you calculate log78.34log_7 8.34 with a calculator?