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

The answer to 5^{x-2}=3*2^{2x+3} is x=(ln(600))/(ln(5)-2ln(2))

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

The solution is x=(ln(600))/(ln(5)-2ln(2))

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

x = \frac{ln ( 600 )}{ln ( 5 ) - 2 ln ( 2 )}

Decimal Notation

x = 28.66732 \dots

Solution steps

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

Apply exponent rules

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

Solve

(x - 2) ln (5) = ln (3) + (2 x + 3) ln (2) : x = \frac{ln ( 600 )}{ln ( 5 ) - 2 ln ( 2 )}

x = \frac{ln ( 600 )}{ln ( 5 ) - 2 ln ( 2 )}

3^{- x} = 2

15 + 4^{x} = 31

2^{2 x} - 3 \cdot 2^{x + 2} + 32 = 0

1 \cdot 1 0^{x} = 3

4^{x} + 2^{x} = 8

What is the answer to 5^{x-2}=3*2^{2x+3} ?
The answer to 5^{x-2}=3*2^{2x+3} is x=(ln(600))/(ln(5)-2ln(2))
Solve for x: 5^{x-2}=3*2^{2x+3}
The solution is x=(ln(600))/(ln(5)-2ln(2))