What is the answer to 6(4^x)=5(3^{2x-3}) ?

The answer to 6(4^x)=5(3^{2x-3}) is x=-(ln(162)-ln(5))/(2(ln(2)-ln(3)))

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

The solution is x=-(ln(162)-ln(5))/(2(ln(2)-ln(3)))

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

x = - \frac{ln ( 162 ) - ln ( 5 )}{2 ( ln ( 2 ) - ln ( 3 ) )}

Decimal Notation

x = 4.28909 \dots

Solution steps

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

Apply exponent rules

ln (6) + x ln (4) = ln (5) + (2 x - 3) ln (3)

Solve

ln (6) + x ln (4) = ln (5) + (2 x - 3) ln (3) : x = - \frac{ln ( 162 ) - ln ( 5 )}{2 ( ln ( 2 ) - ln ( 3 ) )}

x = - \frac{ln ( 162 ) - ln ( 5 )}{2 ( ln ( 2 ) - ln ( 3 ) )}

e^{2 x} = 1

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

e^{7 - 4 x} = 6

3^{x} = 27

7 (4^{x}) = 4 (6^{2 x - 2})

What is the answer to 6(4^x)=5(3^{2x-3}) ?
The answer to 6(4^x)=5(3^{2x-3}) is x=-(ln(162)-ln(5))/(2(ln(2)-ln(3)))
Solve for x: 6(4^x)=5(3^{2x-3})
The solution is x=-(ln(162)-ln(5))/(2(ln(2)-ln(3)))