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How do you solve ${log}_{2} x^{7} = 21$ $Log_2 x^7=21$ ?

1 Answer

May 28, 2016

$x = 8$ $x=8$

Explanation:

Using basic properties of logs we find:

$21 = {log}_{2} x^{7} = 7 {log}_{2} x$ $21 = log_2 x^7 = 7 log_2 x$

Dividing both ends by $7$ $7$ we have:

$3 = {log}_{2} x$ $3 = log_2 x$

So:

$2^{3} = 2^{{log}_{2} x} = x$ $2^3 = 2^(log_2 x) = x$

That is:

$x = 2^{3} = 8$ $x = 2^3 = 8$

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