SOLUTION: Rewrite each expression in exponential form and determine the value of x. (a) log49 x=1/2 (b) log9 27 = x

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Question 149400: Rewrite each expression in exponential form and determine the value of x.
(a) log49 x=1/2
(b) log9 27 = x
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Rewrite each expression in exponential form and determine the value of x.
(a) log49 x=1/2
x = 49^(1/2) = 7
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(b) log9 27 = x
9^x = 27
3^2x = 3^3
2x = 3
x = 3/2
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Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)

log%2849%2C%28x%29%29=1%2F2 Start with the given equation.


Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> b%5Ey=x


Convert from rational notation to radical notation.


Take the square root of 49 to get 7. Note: only the positive square root is considered in this case.


So the answer is x=7




b)

log%289%2C%2827%29%29=x Start with the given equation.


9%5Ex=27 Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> b%5Ey=x


%283%5E2%29%5Ex=3%5E3 Rewrite 9 as 3%5E2 and 27 as 3%5E3


3%5E%282x%29=3%5E3 Multiply the exponents.


2x=3 Since the bases are equal, the exponents are equal.


x=3%2F2 Divide both sides by 2.


So the answer is x=3%2F2