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

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

Solve for x: sqrt(5^{4x+2)}=7^{x+5}

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

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

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

Decimal Notation

x = 6.37889 \dots

Solution steps

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

Apply exponent rules

(4 x + 2) \frac{1}{2} ln (5) = (x + 5) ln (7)

Solve

(4 x + 2) \frac{1}{2} ln (5) = (x + 5) ln (7) : x = \frac{5 ln ( 7 ) - ln ( 5 )}{2 ln ( 5 ) - ln ( 7 )}

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

2^{2 x} + 2^{x + 2} = 32

243 = 3^{\frac{m}{10}}

9^{x} - 16 \cdot 3^{x} + 27 = 0

3 e^{x} - x e^{x} = 0

2 5^{2 x + 1} - 1 = 143

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