SOLUTION: how do I solve 10^log base2 x=3

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Question 735095: how do I solve
10^log base2 x=3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
10%5Elog%282%2C+%28x%29%29=3
One possible solution:
Find the base 10 log of each side:
log%28%2810%5Elog%282%2C+%28x%29%29%29%29=log%28%283%29%29
Now we can use a property of logarithms, log%28a%2C+%28p%5En%29%29+=+n%2Alog%28a%2C+%28p%29%29, to rewrite the left side:
log%282%2C+%28x%29%29%2Alog%28%2810%29%29=log%28%283%29%29
One of the properties of logarithms you should have learned is:
log%28a%2C+%28a%29%29+=+1
So log(10) = 1:
log%282%2C+%28x%29%29=log%28%283%29%29
Now we rewrite the equation in exponential form. In general log%28a%2C+%28p%29%29+=+n is equivalent to p+=+a%5En. Using this pattern on our equation we get:
x=2%5Elog%28%283%29%29

If you want/need a decimal approximation for this answer then just enter the expression on the right side into your calculator.