How do you write $3 {log}_{4} 16 = 2$ $3log_(4)16=2$ in exponential form?

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How do you write $3 {log}_{4} 16 = 2$ $3log_(4)16=2$ in exponential form?

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Answer 1 · 2015-09-30T14:04:27

$4^{2} = 16$ $4^2=16$

Explanation:

According to the definition of log:
$y = {log}_{b} x$ $y=log_bx$ is equivalent to $b^{y} = x$ $b^y=x$

So we have:
$3 {log}_{4} (16) = 2$ $3log_(4)(16)=2$
${log}_{4} (16^{3}) = 2$ $log_(4)(16^3)=2$

Compare what we have to the definition of log:
$y = 2$ $y=2$
$b = 4$ $b=4$
$x = 16^{3}$ $x=16^3$

Therefore:
$4^{2} = 16^{3}$ $4^2=16^3$

However, $4^{2}$ $4^2$ is definitely not equal to $16^{3}$ $16^3$ . I think you probably meant " ${log}_{4} (16) = 2$ $log_4(16)=2$ " instead, which would have resulted to the answer $4^{2} = 16$ $color(blue)(4^2=16)$ .

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How do you write $3 {log}_{4} 16 = 2$ $3log_(4)16=2$ in exponential form?

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