What is the answer to 2^{x+2}=5^{x-3} ?

The answer to 2^{x+2}=5^{x-3} is x=(ln(500))/(ln(5)-ln(2))

Solve for x: 2^{x+2}=5^{x-3}

The solution is x=(ln(500))/(ln(5)-ln(2))

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2^{x + 2} = 5^{x - 3}

x = \frac{ln ( 500 )}{ln ( 5 ) - ln ( 2 )}

Decimal Notation

x = 6.78235 \dots

Solution steps

2^{x + 2} = 5^{x - 3}

Apply exponent rules

(x + 2) ln (2) = (x - 3) ln (5)

Solve

(x + 2) ln (2) = (x - 3) ln (5) : x = \frac{ln ( 500 )}{ln ( 5 ) - ln ( 2 )}

x = \frac{ln ( 500 )}{ln ( 5 ) - ln ( 2 )}

2 = 3 e^{4 x}

\frac{1}{e ^{x}} = e^{- x}

e^{x + 5} = 5

3^{x} - 14 \cdot 3^{- x} = 5

4^{2 x - 5} = 65

What is the answer to 2^{x+2}=5^{x-3} ?
The answer to 2^{x+2}=5^{x-3} is x=(ln(500))/(ln(5)-ln(2))
Solve for x: 2^{x+2}=5^{x-3}
The solution is x=(ln(500))/(ln(5)-ln(2))