What is the answer to 4^{2x}=5^{2x-1} ?

The answer to 4^{2x}=5^{2x-1} is x=-(ln(5))/(2(2ln(2)-ln(5)))

Solve for x: 4^{2x}=5^{2x-1}

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

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4^{2 x} = 5^{2 x - 1}

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

Decimal Notation

x = 3.60628 \dots

Solution steps

4^{2 x} = 5^{2 x - 1}

Apply exponent rules

2 x ln (4) = (2 x - 1) ln (5)

Solve

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

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

6 4^{3 x} = 51 2^{2 x + 12}

8^{x + 2} = (\frac{1}{32})^{- 5 x}

\frac{1}{4 ^{x}} = \frac{1}{64}

e^{x + 2} = 3^{x}

2 5^{x} - 2 \cdot 5^{x} - 8 = 0

What is the answer to 4^{2x}=5^{2x-1} ?
The answer to 4^{2x}=5^{2x-1} is x=-(ln(5))/(2(2ln(2)-ln(5)))
Solve for x: 4^{2x}=5^{2x-1}
The solution is x=-(ln(5))/(2(2ln(2)-ln(5)))