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bekas [8.4K]
3 years ago
8

Find the Domain of the following exponential and logarithmic equations and solve them:

Mathematics
1 answer:
kakasveta [241]3 years ago
5 0

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

\log_{\frac1x}243=5

Write both sides as powers of 1/<em>x</em> :

\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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