What is the answer to 4^{5x}=7^{x+3} ?

The answer to 4^{5x}=7^{x+3} is x=(3ln(7))/(10ln(2)-ln(7))

Solve for x: 4^{5x}=7^{x+3}

The solution is x=(3ln(7))/(10ln(2)-ln(7))

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4^{5 x} = 7^{x + 3}

x = \frac{3 ln ( 7 )}{10 ln ( 2 ) - ln ( 7 )}

Decimal Notation

x = 1.17092 \dots

Solution steps

4^{5 x} = 7^{x + 3}

Apply exponent rules

5 x ln (4) = (x + 3) ln (7)

Solve

5 x ln (4) = (x + 3) ln (7) : x = \frac{3 ln ( 7 )}{10 ln ( 2 ) - ln ( 7 )}

x = \frac{3 ln ( 7 )}{10 ln ( 2 ) - ln ( 7 )}

e^{2 x} + 3 e^{x} - 4 = 0

\frac{2 5 ^{x}}{5} = 1

\frac{2 5 ^{x}}{5 ^{x + 4}} = 2 5^{1 - x}

3^{2 x + 3} = 3

e^{x^{2} - 1} = 1

What is the answer to 4^{5x}=7^{x+3} ?
The answer to 4^{5x}=7^{x+3} is x=(3ln(7))/(10ln(2)-ln(7))
Solve for x: 4^{5x}=7^{x+3}
The solution is x=(3ln(7))/(10ln(2)-ln(7))