What is the answer to 7^{9x-2}=10^{3x+6} ?

The answer to 7^{9x-2}=10^{3x+6} is x=(6ln(10)+2ln(7))/(3(-ln(10)+3ln(7)))

Solve for x: 7^{9x-2}=10^{3x+6}

The solution is x=(6ln(10)+2ln(7))/(3(-ln(10)+3ln(7)))

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7^{9 x - 2} = 1 0^{3 x + 6}

x = \frac{6 ln ( 10 ) + 2 ln ( 7 )}{3 ( - ln ( 10 ) + 3 ln ( 7 ) )}

Decimal Notation

x = 1.66964 \dots

Solution steps

7^{9 x - 2} = 1 0^{3 x + 6}

Apply exponent rules

(9 x - 2) ln (7) = (3 x + 6) ln (10)

Solve

(9 x - 2) ln (7) = (3 x + 6) ln (10) : x = \frac{6 ln ( 10 ) + 2 ln ( 7 )}{3 ( - ln ( 10 ) + 3 ln ( 7 ) )}

x = \frac{6 ln ( 10 ) + 2 ln ( 7 )}{3 ( - ln ( 10 ) + 3 ln ( 7 ) )}

1 6^{- x + 27} = 3 2^{x}

x y^{^{'}} + 5 y = \frac{2 e ^{- 2 x}}{x ^{3}}

4^{x + 3} \times 8^{2 x - 1} = 2

5^{2 x + 1} + 3 \cdot 5^{6 x - 3} = 500

3 e^{3 x + 4} + 8 = e

What is the answer to 7^{9x-2}=10^{3x+6} ?
The answer to 7^{9x-2}=10^{3x+6} is x=(6ln(10)+2ln(7))/(3(-ln(10)+3ln(7)))
Solve for x: 7^{9x-2}=10^{3x+6}
The solution is x=(6ln(10)+2ln(7))/(3(-ln(10)+3ln(7)))