Solve the logarithmic equation loga(y)+3loga(2)=5

 Exercise

$\log_a\left(y\right)+3\log_a\left(2\right)=5$

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Apply the formula: $a\log_{b}\left(x\right)$$=\log_{b}\left(x^a\right)$, where $a=3$, $b=a$ and $x=2$

$\log_{a}\left(y\right)+\log_{a}\left(8\right)=5$

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The sum of two logarithms of the same base is equal to the logarithm of the product of the arguments

$\log_{a}\left(8y\right)=5$

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Take the variable outside of the logarithm

$a^{\log_{a}\left(8y\right)}=a^5$

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Simplifying the logarithm

$8y=a^5$

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Divide both sides of the equation by $8$

$y=\frac{a^5}{8}$

$y=\frac{a^5}{8}$

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