How do you evaluate ${log}_{49} 343$ $log_49 343$ ?

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How do you evaluate ${log}_{49} 343$ $log_49 343$ ?

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Answer 1 · 2018-05-25T11:52:59

${log}_{49} 343 = \frac{3}{2}$ $log_49 343 = 3/2$

Explanation:

${log}_{49} 343$ $log_49 343$
$= \frac{{log}_{7} (343)}{{log}_{7} (49)}$ $=log_7(343)/log_7(49)$
$= \frac{{log}_{7} (7^{3})}{{log}_{7} (7^{2})}$ $=log_7(7^3)/log_7(7^2)$
$= \frac{3 {log}_{7} (7)}{2 {log}_{7} (7)}$ $=(3log_7(7))/(2log_7(7))$
$= \frac{3}{2}$ $=3/2$

Alternatively, you could say $343 = 49^{\frac{3}{2}}$ $343 = 49 ^ (3/2)$

The answer will follow immediately.

Answer 2 · 2018-05-26T08:36:45

${log}_{49} 343 = \frac{3}{2}$ $log_(49)343=3/2$

Explanation:

$x = {log}_{49} 343$ $x=log_(49)343$

$\Rightarrow 49^{x} = 343$ $=>49^x=343$

$\Rightarrow {(7^{2})}^{x} = 343$ $=>(7^2)^x=343$

$7^{2 x} = 343$ $7^(2x)=343$

but $7^{3} = 343$ $7^3=343$

$:.2x=3$

$=>x=3/2$

$log_(49)343=3/2$

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How do you evaluate ${log}_{49} 343$ $log_49 343$ ?

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