Question 1204567
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{{{log(2,(8*sqrt(2)))}}} would be written out as log(2, 8*sqrt(2) )
Or you could say "log base 2 of 8*sqrt(2)" 



Here is one approach.
{{{log(2,(8*sqrt(2))) = x}}}


{{{2^x = 8*sqrt(2)}}} Convert the equation to exponential form


{{{2^x = 2^3*(2)^(1/2)^""}}} Rewrite 8 as 2^3. Rewrite the square root as an exponent of 1/2.


{{{2^(x) = 2^(3+1/2)^""}}} Use the rule that a^b*a^c = a^(b+c)


{{{2^(x) = 2^(7/2)^""}}}


{{{x = 7/2}}} Since the bases are equal, the exponents must be equal.


Another approach would be to use the change of base formula similar to what was done on this question
<a href = "https://www.algebra.com/algebra/homework/logarithm/logarithm.faq.question.1204568.html">https://www.algebra.com/algebra/homework/logarithm/logarithm.faq.question.1204568.html</a>


As quick confirmation, use a calculator to find that
log( 8*sqrt(2) )/log(2) = 3.5
and
7/2 = 3.5
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