SOLUTION: Hello I need some help solving a logarithm such as: 4^(7+3x)=1/16

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Question 538256: Hello I need some help solving a logarithm such as:
4^(7+3x)=1/16
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
x=b%5Ey is the same as y+=+log%28b%2Cx%29


That's the definition of logarithms.
The problem gives 1%2F6=4%5E%287%2B3x%29 which is the same as 7%2B3x+=+log%284%2C1%2F16%29


Look at the right side. log%284%2C1%2F16%29


Back to the definition of logarithms. Turn it into an equation because now we want to find its value.


y=log%284%2C1%2F16%29 means 1%2F16+=+4%5Ey


1%2F%284%5E2%29=1%2F16


Remember that x%5E%28-y%29+=+1%2Fx%5Ey.


So the answer is y=-2 because 4%5E-2+=+1%2F16


-2=log%284%2C1%2F16%29 so substitute -2 into the right side of the equation.


7%2B3x+=+-2


Subtract 7 from both sides, then divide both sides by 3.


x=-3


Check the original equation.


4%5E%287%2B3%28-3%29%29=+4%5E%287-9%29+=+4%5E-2+=+1%2F16

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