SOLUTION: Use common or natural logarithms to solve the exponential equation symbolically.
4^(7-3x)=1/16
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Question 606283: Use common or natural logarithms to solve the exponential equation symbolically.
4^(7-3x)=1/16
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
}\ =\ \frac{1}{16})
The trick here is to note that 
Then you can write:
}\ =\ 4^{-2})
Now you really don't have to actually mess with taking the log of both sides. Since the bases are equal you can simply equate the exponents. But in the interest of never being so stupid as to not follow your math teacher's instructions, herewith the logarithm way. I use natural logs but you can use any base you like and the result will be the same.
}\right)\ =\ \ln\left(4^{-2}\right))
Then use
\ =\ n\log_b(x))
to write:
\ln\left(4\right) \ =\ -2\ln\left(4\right))
Then divide both sides by )
(Do you see why )
would have worked regardless of the value of the logarithm base?)
Just solve for 
. Don't forget to check your answer.
John
My calculator said it, I believe it, that settles it
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