What is the answer to 3(4^x)=5(7^{2x-2}) ?

The answer to 3(4^x)=5(7^{2x-2}) is x=-(ln(147)-ln(5))/(2(ln(2)-ln(7)))

Solve for x: 3(4^x)=5(7^{2x-2})

The solution is x=-(ln(147)-ln(5))/(2(ln(2)-ln(7)))

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3 (4^{x}) = 5 (7^{2 x - 2})

x = - \frac{ln ( 147 ) - ln ( 5 )}{2 ( ln ( 2 ) - ln ( 7 ) )}

Decimal Notation

x = 1.34941 \dots

Solution steps

3 (4^{x}) = 5 (7^{2 x - 2})

Apply exponent rules

ln (3) + x ln (4) = ln (5) + (2 x - 2) ln (7)

Solve

ln (3) + x ln (4) = ln (5) + (2 x - 2) ln (7) : x = - \frac{ln ( 147 ) - ln ( 5 )}{2 ( ln ( 2 ) - ln ( 7 ) )}

x = - \frac{ln ( 147 ) - ln ( 5 )}{2 ( ln ( 2 ) - ln ( 7 ) )}

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

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

e^{2 x} = 1

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

e^{7 - 4 x} = 6

What is the answer to 3(4^x)=5(7^{2x-2}) ?
The answer to 3(4^x)=5(7^{2x-2}) is x=-(ln(147)-ln(5))/(2(ln(2)-ln(7)))
Solve for x: 3(4^x)=5(7^{2x-2})
The solution is x=-(ln(147)-ln(5))/(2(ln(2)-ln(7)))