Mathematics: Need help pls will mark brainliest

The base of a logarithm should always be positive and can t be equal to 1, so the domain is 0 x 1 or x 1.Write both sides as powers of 1/x :Recall that , so thatTake the 5th root of both sides, recalling that 3⁵ = 243, so...

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aloading6574

31.03.2021

Mathematics

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m jmn

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lilly9645

31.03.2021

Mathematics

y = (2/7)x - 7

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kcarstensen59070

14.07.2022

Mathematics

The base of a logarithm should always be positive and can't be equal to 1, so the domain is 0 < x < 1 or x > 1.

$\log_{\frac1x}243=5$

Write both sides as powers of 1/x :

$\left(\dfrac1x\right)^{\log_{\frac1x}243}=\left(\dfrac1x\right)^5$

Recall that $a^{\log_ab}=b$ , so that

$243=\left(\dfrac1x\right)^5$

$243=\dfrac1{x^5}$

$x^5=\dfrac1{243}$

Take the 5th root of both sides, recalling that 3⁵ = 243, so

$x=\sqrt[5]{\dfrac1{243}}=\boxed{\dfrac13}$

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