SOLUTION: Solve the exponential equation using like bases. 64^x-5=256^5x+1

SOLUTION: Solve the exponential equation using like bases. 64^x-5=256^5x+1 - Show step by step.

Question 1005697: Solve the exponential equation using like bases. 64^x-5=256^5x+1 - Show step by step.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
64^x-5=256^5x+1
64=2^6
Therefore, 64^x-5=(2^6)^(x-5)=2^(6x-30) by product rule of exponents.
256^(5x+1)
256=2^8
Therefore, (2^8)^(5x+1)=2^(40x+8)
Set the two equal
40x+8=6x-30. You can do this by taking log 2 of both sides, which removes the base and makes it 1, log 10 10=1
Solving the above, 34x=-22
x=-(22/34) or -11/17
using common denominators in exponents to check
64^(-11-85)/17=64^(-96/17)=6.35 X 10^-11
256^(-55-17)/17=256^(-72/17)=6.35 x 10^-11

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