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# Find the value of ‘x’ if 3log 2 + $\dfrac{1}{3}$log27 – log4 = log x.

Last updated date: 28th Mar 2023
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Hint: To solve the logarithmic equation given in the question we use the formulae for logarithmic functions and simplify for the answer.

Given data, 3log 2 + $\dfrac{1}{3}$log27 – log4 = log x
⟹3log 2 +$\dfrac{1}{3}$ log ${3^3}$ – log ${2^2}$ = log x (27 = ${3^3}$ and 4 =${2^2}$)
⟹3 log 2 + ($\dfrac{1}{3}$) × 3 log 3 – 2log2 = log x -- (log ${{\text{x}}^{\text{y}}}$ = y log x)