What is the answer to solvefor x,5^{8x}=8^{8x-5} ?

The answer to solvefor x,5^{8x}=8^{8x-5} is x=-(15ln(2))/(8(ln(5)-3ln(2)))

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solvefor x,5^{8x}=8^{8x-5}

solve for

x, 5^{8 x} = 8^{8 x - 5}

x = - \frac{15 ln ( 2 )}{8 ( ln ( 5 ) - 3 ln ( 2 ) )}

Decimal Notation

x = 2.76519 \dots

Solution steps

5^{8 x} = 8^{8 x - 5}

Apply exponent rules

8 x ln (5) = (8 x - 5) ln (8)

Solve

8 x ln (5) = (8 x - 5) ln (8) : x = - \frac{15 ln ( 2 )}{8 ( ln ( 5 ) - 3 ln ( 2 ) )}

x = - \frac{15 ln ( 2 )}{8 ( ln ( 5 ) - 3 ln ( 2 ) )}

75 = 3 3^{x}

4^{x} = 3 (2)^{x}

3^{(1 + 2 x)} = 27

2^{n} = 40

3^{2 x + 5} = 81

What is the answer to solvefor x,5^{8x}=8^{8x-5} ?
The answer to solvefor x,5^{8x}=8^{8x-5} is x=-(15ln(2))/(8(ln(5)-3ln(2)))