How do you evaluate ${log}_{7} (343)$ $log_7(343)$ ?

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Answer 1 · 2015-11-29T01:01:34

${log}_{7} (343) = 3$ $log_7(343) = 3$

If $x = {log}_{7} (343)$ $x=log_7(343)$
then we are looking for a value of $x$ $x$ such that $7^{x} = 343$ $7^x= 343$

$7^{1} = 7$ $7^1=7$
$7^{2} = 49$ $7^2=49$
$7^{3} = 343$ $7^3=343$

$\Rightarrow x = 3$ $rArr x=3$

In most cases a question like this would require the use of a calculator. In this case the question was obviously set up for a direct solution.

Answer 2 · 2015-11-30T14:06:25

3

${log}_{7} (343) = {log}_{7} (7^{3})$ $log_7(343)=log_7(7^3)$
$= 3 {log}_{7} (7)$ $=3log_7(7)$
$= 3 \cdot 1$ $=3*1$
$= 3$ $=3$

How do you evaluate log7(343)log_7(343)?