What is the answer to 5^x=9*4^x ?

The answer to 5^x=9*4^x is x=(2ln(3))/(ln(5)-2ln(2))

Solve for x: 5^x=9*4^x

The solution is x=(2ln(3))/(ln(5)-2ln(2))

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5^{x} = 9 \cdot 4^{x}

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

Decimal Notation

x = 9.84668 \dots

Solution steps

5^{x} = 9 \cdot 4^{x}

Apply exponent rules

x ln (5) = ln (9) + x ln (4)

Solve

x ln (5) = ln (9) + x ln (4) : x = \frac{2 ln ( 3 )}{ln ( 5 ) - 2 ln ( 2 )}

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

4^{5 p - 1} = 8^{p - 2}

\frac{1}{2} (3)^{x} = \frac{9}{2}

8 1^{2^{x + 7}} = 3^{8^{x - 13}}

x, e^{2 x} - 11 e^{x} + 30 = 0

3^{2 x} - 3^{x} - 2 = 0

What is the answer to 5^x=9*4^x ?
The answer to 5^x=9*4^x is x=(2ln(3))/(ln(5)-2ln(2))
Solve for x: 5^x=9*4^x
The solution is x=(2ln(3))/(ln(5)-2ln(2))