Question #87c76

1 Answer
Prof_S
Jan 24, 2016

x = #1/2 log (50/3)#, where the logarithm is base 2.

Explanation:

#4^x# is equal to #2^(2x)#, so the equation can be written as #2^(2x)+2^(1+2x) = 50#. Factoring out #2^(2x)#, one gets #2^(2x)(1+2)=2^(2x)(3)=50#, which is equivalent to #2^(2x)=50/3#. Taking the logarithm base 2 of both sides gives #2x = log (50/3)# or, equivalently, #x = 1/2 log (50/3)#, where the logarithm is base 2.

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