What is the answer to 5^{x-4}=7^{5x+2} ?

The answer to 5^{x-4}=7^{5x+2} is x=(2ln(7)+4ln(5))/(ln(5)-5ln(7))

Solve for x: 5^{x-4}=7^{5x+2}

The solution is x=(2ln(7)+4ln(5))/(ln(5)-5ln(7))

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5^{x - 4} = 7^{5 x + 2}

x = \frac{2 ln ( 7 ) + 4 ln ( 5 )}{ln ( 5 ) - 5 ln ( 7 )}

Decimal Notation

x = - 1.27209 \dots

Solution steps

5^{x - 4} = 7^{5 x + 2}

Apply exponent rules

(x - 4) ln (5) = (5 x + 2) ln (7)

Solve

(x - 4) ln (5) = (5 x + 2) ln (7) : x = \frac{2 ln ( 7 ) + 4 ln ( 5 )}{ln ( 5 ) - 5 ln ( 7 )}

x = \frac{2 ln ( 7 ) + 4 ln ( 5 )}{ln ( 5 ) - 5 ln ( 7 )}

\frac{( 4 ^{x} + 4 )}{5} = 2^{x}

7^{3 x - 17} = 4 9^{x}

(- 8)^{x} = - 125

1 2^{b} = 3

2^{n} = 6

What is the answer to 5^{x-4}=7^{5x+2} ?
The answer to 5^{x-4}=7^{5x+2} is x=(2ln(7)+4ln(5))/(ln(5)-5ln(7))
Solve for x: 5^{x-4}=7^{5x+2}
The solution is x=(2ln(7)+4ln(5))/(ln(5)-5ln(7))