How do you evaluate $log_343 (7)$ ?

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Answer 1 · 2016-09-23T02:54:21

$log_343(7)=1/3$

$log_343(7)=x$

Step 1: Rewrite as an exponential.
$343^x=7$

Step 2:Take the log of both sides.
$log343^x=log7$

Step 3: Use the log rule $loga^x=xloga$ .
$xlog343=log7$

$x=log7/log343color(white)(aaaa)$ Use a calculator
$x=1/3$

OR

Use the change of base formula $log_ba=loga/logb$
$log_343(7)=log7/log343=1/3color(white)(aaa)$ Use a calculator

OR

Rewrite as an exponential and consider the powers of 7.
$343^x=7$

$343=7^3$ or $root(3)343=7$ or $343^(1/3)=7$
$x=1/3$

How do you evaluate log_343 (7)log_343 (7)?