SOLUTION: Solve the following equation for x:
6^(x-4)=7^(-7x)
Write your answer as an expression involving base-10 logarithms.
Algebra.Com
Question 254226: Solve the following equation for x:
6^(x-4)=7^(-7x)
Write your answer as an expression involving base-10 logarithms.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Take the base-10 log of both sides:
\ =\ \log\left(7^{-7x}\right))
Apply
\ =\ n\log_b(x))
to write:
\log\left(6\right)\ =\ -7x\cdot\log\left(7\right))
Multiply both sides by })
}{\log(6)}\right)x)
Add }{\log(6)}\right)x)
to both sides:
}{\log(6)}\right)x\ =\ 4)
Factor the LHS:
}{\log(6)}\right)\ =\ 4)
Multiply both sides by the reciprocal of the constant coefficient in the LHS:
}{\log(6)\ +\ 7\cdot\log(7)}\ \approx\ 0.464996)
John
RELATED QUESTIONS
Solve for x.
6^(-7x)=17^(-x-3)
Write the exact answer using base-10 logarithms (answered by lwsshak3)
solve for x
12^(-7x)=7^(-x+8)
give the exact answer using base 10... (answered by stanbon)
Solve for x.
2^x-6=7^2x
Write the exact answer using base-10 logarithms.... (answered by Alan3354,solver91311)
solve for x
3^(x-7)=14^(2x)
write the exact answer using base-10... (answered by Alan3354,tommyt3rd)
Solve for x
8^(2x)=13^(x+10)
Write the exact answer using base-10... (answered by lwsshak3)
Solve for X:
9 ^(-x-3) = 14 ^(-4x)
Write the exact answer using base-10... (answered by htmentor)
Solve for x.
17^(5x)=11^(x-9)
Write the exact answer using base-10... (answered by jim_thompson5910)
solve for x.
15^(8x)=16^(x+8)
Write the exact answer using base-10 logarithms. (answered by josgarithmetic)
Solve the equation
e^7x/2= 5 for x: Express your answer in terms of... (answered by lwsshak3)