What is the answer to (9^{2x-3})/(3^{x-2)}=256 ?

The answer to (9^{2x-3})/(3^{x-2)}=256 is x=(8ln(2)+4ln(3))/(3ln(3))

Solve for x: (9^{2x-3})/(3^{x-2)}=256

The solution is x=(8ln(2)+4ln(3))/(3ln(3))

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\frac{9 ^{2 x - 3}}{3 ^{x - 2}} = 256

x = \frac{8 ln ( 2 ) + 4 ln ( 3 )}{3 ln ( 3 )}

Decimal Notation

x = 3.01581 \dots

Solution steps

\frac{9 ^{2 x - 3}}{3 ^{x - 2}} = 256

Apply exponent rules

(2 (2 x - 3) - x + 2) ln (3) = ln (256)

Solve

(2 (2 x - 3) - x + 2) ln (3) = ln (256) : x = \frac{8 ln ( 2 ) + 4 ln ( 3 )}{3 ln ( 3 )}

x = \frac{8 ln ( 2 ) + 4 ln ( 3 )}{3 ln ( 3 )}

Verify Solutions:

x = \frac{8 ln ( 2 ) + 4 ln ( 3 )}{3 ln ( 3 )}

True

The solution is

x = \frac{8 ln ( 2 ) + 4 ln ( 3 )}{3 ln ( 3 )}

2^{4 x} = 2^{2 x - 3}

5^{5 x + 1} = 2^{x - 3}

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

81 = 3^{x^{4}}

4 9^{3 y} = 7^{y + 1}

What is the answer to (9^{2x-3})/(3^{x-2)}=256 ?
The answer to (9^{2x-3})/(3^{x-2)}=256 is x=(8ln(2)+4ln(3))/(3ln(3))
Solve for x: (9^{2x-3})/(3^{x-2)}=256
The solution is x=(8ln(2)+4ln(3))/(3ln(3))