Find the logarithm of 181\dfrac{1}{81}811 to the base 27.
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Let,
⇒log27 (181)=x⇒181=27x⇒(134)=(33)x⇒3−4=33x⇒3x=−4⇒x=−43.\Rightarrow \text{log}_{27} \space \Big(\dfrac{1}{81}\Big) = x \\[1em] \Rightarrow \dfrac{1}{81} = 27^x \\[1em] \Rightarrow \Big(\dfrac{1}{3^4}\Big) = (3^3)^x \\[1em] \Rightarrow 3^{-4} = 3^{3x} \\[1em] \Rightarrow 3x = -4 \\[1em] \Rightarrow x = -\dfrac{4}{3}.⇒log27 (811)=x⇒811=27x⇒(341)=(33)x⇒3−4=33x⇒3x=−4⇒x=−34.
Hence, required value = −43-\dfrac{4}{3}−34.
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Find the logarithm of 116\dfrac{1}{16}161 to the base 4.
Find the logarithm of 27 to the base 9.
State, true or false :
If log10 x = a, then 10x = a
If xy = z, then y = logz x
