SOLUTION: Solve for x.
2^x-6=7^2x
Write the exact answer using base-10 logarithms.
Please help and explain!
Algebra.Com
Question 1037819: Solve for x.
2^x-6=7^2x
Write the exact answer using base-10 logarithms.
Please help and explain!
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
What's the exponent of 2?
x ?
or x-6 ?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Rules needed:
\ =\ n\cdot\log(x))
\ =\ \log_c(b))
The sum of the logs is the log of the product. The difference of the logs is the log of the quotient.
Definition: \ =\ \log_{10}(x))
==================================================================
\ =\ \log\left(7^{2x}\right))
\log\left(2\right)\ =\ x\log\left(7^2\right))
\ -\ 6\log\left(2\right)\ =\ x\log\left(49\right))
\ -\ x\log\left(49\right)\ =\ 6\log\left(2\right))
\ -\ \log\left(49\right)\right)\ =\ \log\left(2^6\right))
}{\log\left(2\right)\ -\ \log\left(49\right)})
}{\log\left(\frac{2}{49}\right)})
John
My calculator said it, I believe it, that settles it
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