SOLUTION: Please help me solve this equation. {{{log_b sqrt(b^3)}}}

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Question 326879: Please help me solve this equation. log_b+sqrt%28b%5E3%29
Found 2 solutions by Fombitz, jessica43:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
It's not an equation because there's no equal sign.
It's an expression and you can simplify it.
log%28b%2C+%28sqrt%28b%5E3%29%29%29=log%28b%2C%28b%5E%283%2F2%29%29%29
log%28b%2C+%28sqrt%28b%5E3%29%29%29=%283%2F2%29log%28b%2C%28b%29%29
log%28b%2C+%28sqrt%28b%5E3%29%29%29=%283%2F2%29%281%29
log%28b%2C+%28sqrt%28b%5E3%29%29%29=highlight%28%283%2F2%29%29

Answer by jessica43(140) About Me  (Show Source):
You can put this solution on YOUR website!
To solve this problem, you are going to need to use the base b logarithm formula to rewrite the problem:
log[base b]a = c means the same as b^c = a
So use this in your problem:
log[b] sqrt(b^3) = x
a = sqrt(b^3), b = b, c = x
Now rewrite as the exponent:
b^c = a
b^x = sqrt(b^3)
The square root of b^3 can be rewritten as b^(3/2) (rule of fractional exponents), so:
b^x = b^(3/2)
So x = 3/2.