What is the answer to solvefor x,2^{4x-9}=9^{7x-4} ?

The answer to solvefor x,2^{4x-9}=9^{7x-4} is x=-(8ln(3)-9ln(2))/(2(2ln(2)-7ln(3)))

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solvefor x,2^{4x-9}=9^{7x-4}

solve for

x, 2^{4 x - 9} = 9^{7 x - 4}

x = - \frac{8 ln ( 3 ) - 9 ln ( 2 )}{2 ( 2 ln ( 2 ) - 7 ln ( 3 ) )}

Decimal Notation

x = 0.20229 \dots

Solution steps

2^{4 x - 9} = 9^{7 x - 4}

Apply exponent rules

(4 x - 9) ln (2) = (7 x - 4) ln (9)

Solve

(4 x - 9) ln (2) = (7 x - 4) ln (9) : x = - \frac{8 ln ( 3 ) - 9 ln ( 2 )}{2 ( 2 ln ( 2 ) - 7 ln ( 3 ) )}

x = - \frac{8 ln ( 3 ) - 9 ln ( 2 )}{2 ( 2 ln ( 2 ) - 7 ln ( 3 ) )}

lo g_{10} (10 0^{x}) = 35

3 = 60 (2 - 60) e^{- 0.001 x}

3^{x + 5} = 7

5^{x} + 5^{x + 1} + 5^{x + 2} = 155

e^{x} + e^{- x} = 7.4533

What is the answer to solvefor x,2^{4x-9}=9^{7x-4} ?
The answer to solvefor x,2^{4x-9}=9^{7x-4} is x=-(8ln(3)-9ln(2))/(2(2ln(2)-7ln(3)))