Logarithm...

Algebra Level 1

log ⁡ a 81 = 8 \large \log_a 81 = 8

Which is true for a ? a?

a < 1 a < 1 a < 0 a <0 a > 4 a > 4 a < 2 a < 2 a > 3 a > 3

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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2 solutions

Jerry McKenzie
Jan 10, 2018

l o g a 81 = 8 ⇒ a 8 = 81 [ [ a > 0 ] ] ⇒ a 8 = 3 4 [ [ a > 0 ] ] ⇒ a = 3 log_{a} 81= 8\\ \Rightarrow a^8 = 81 [[a>0]]\\ \Rightarrow a^8=3^4 [[a>0]] \\ \Rightarrow a=\sqrt{3}

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Uros Stojkovic
Jan 10, 2018

log ⁡ a 81 = 8 log ⁡ 3 81 log ⁡ 3 a = 8 log ⁡ 3 a = 1 2 3 log ⁡ 3 a = 3 1 2 a = 3 ⟹ a < 2 \begin{aligned} \log_{a}81 & = 8 \\ \dfrac{\log_{3}81}{\log_{3}a} & = 8 \\ \log_{3}a &= \frac{1}{2}\\ 3^{\log_{3}a} &= 3^{\frac{1}{2}} \\ a &= \sqrt{3} \\ \implies a &< 2\end{aligned}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

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