SOLUTION: Given that log_2 x=5, evaluate: log_2(4x^2)

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Question 174949: Given that log_2 x=5, evaluate:
log_2(4x^2)
Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Given that log_2 x=5, evaluate:
log_2(4x^2)
-----------
log%282%2Cx%29+=+5
x = 2^5 = 32
-------
log%282%2C4%2A32%5E2%29+=+log%282%2C4096%29
= log%282%2C2%5E12%29
=12

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Given that log_2(x) = 5,
write the exponent equiv
2%5E5 = x
x = 32
:
evaluate:
log_2(4x^2) = y
Substitute 32 for x
log_2(4*32^2) = y
log_2(4*1024) = y
find y
log_2(4096) = y
the exponent equiv:
2%5Ey = 4096
y = 12; we know that 2^12 = 4096