SOLUTION: Make x the subject of this formula: a = b^x

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Question 209259: Make x the subject of this formula:
a = b^x
Found 2 solutions by Theo, RAY100:
Answer by Theo(2967) About Me  (Show Source):
You can put this solution on YOUR website!
a+=+b%5Ex if and only if log%28b%2Ca%29+=+x
example:
8+=+2%5E3 if and only if log%282%2C8%29+=+3
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you can solve for log%282%2C8%29+=+3 using your calculator by converting the base to 10 which the calculator can handle.
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the formula for doing that is:
log%28b%2Cx%29+=+log%28c%2Cx%29%2Flog%28c%2Cb%29
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in this particular case, we have x = 8 and b = 2 and c = 10 and the formula becomes:
log%282%2C8%29+=+log%2810%2C8%29%2Flog%2810%2C2%29
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using your calculator:
log%2810%2C8%29+=+.903089987
and:
log%2810%2C2%29+=+.301029996
so:
log%282%2C8%29+=+log%2810%2C8%29%2Flog%2810%2C2%29
becomes:
log%282%2C8%29+=+.903089987+%2F+.301029996
which becomes:
log%282%2C8%29+=+3
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since you already know that 2%5E3 = 8
then:
log%282%2C8%29+=+3 if and only if 8+=+2%5E3
is confirmed to be a true statement.
and:
8+=+2%5E3 if and only if log%282%2C8%29+=+3
is also confirmed to be a true statement.
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you can start from either one and derive the other.


Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
a=b^x,,,,take log of both sides,,remembering log b^x = x* log b
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log a = x*log b
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log a / log b = x
.
.
check,,let a=3,,b=2,, x= 1.585,,,3=2^1.585,,,,,,ok
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OR,, using the def of exp/ log
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a = b^x,,,becomes,,,,x=log(b) {a},,,,that is log to base b of a,,,
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checking,,, 1.585 = log(b) {a} = log{a} / log(b) = log 3/ log 2,,,ok