What is the answer to 6(4^x)=5(3^{3x-5}) ?

The answer to 6(4^x)=5(3^{3x-5}) is x=(ln(1458)-ln(5))/(3ln(3)-2ln(2))

Solve for x: 6(4^x)=5(3^{3x-5})

The solution is x=(ln(1458)-ln(5))/(3ln(3)-2ln(2))

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6 (4^{x}) = 5 (3^{3 x - 5})

x = \frac{ln ( 1458 ) - ln ( 5 )}{3 ln ( 3 ) - 2 ln ( 2 )}

Decimal Notation

x = 2.97211 \dots

Solution steps

6 (4^{x}) = 5 (3^{3 x - 5})

Apply exponent rules

ln (6) + x ln (4) = ln (5) + (3 x - 5) ln (3)

Solve

ln (6) + x ln (4) = ln (5) + (3 x - 5) ln (3) : x = \frac{ln ( 1458 ) - ln ( 5 )}{3 ln ( 3 ) - 2 ln ( 2 )}

x = \frac{ln ( 1458 ) - ln ( 5 )}{3 ln ( 3 ) - 2 ln ( 2 )}

6 (4^{x}) = 5 (3^{2 x - 3})

e^{2 x} = 1

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

e^{7 - 4 x} = 6

3^{x} = 27

What is the answer to 6(4^x)=5(3^{3x-5}) ?
The answer to 6(4^x)=5(3^{3x-5}) is x=(ln(1458)-ln(5))/(3ln(3)-2ln(2))
Solve for x: 6(4^x)=5(3^{3x-5})
The solution is x=(ln(1458)-ln(5))/(3ln(3)-2ln(2))