What is the answer to 5*6^{x+7}=8*9^{x-10} ?

The answer to 5*6^{x+7}=8*9^{x-10} is x=(20ln(3)+7ln(6)+ln(5)-3ln(2))/(ln(3/2))

Solve for x: 5*6^{x+7}=8*9^{x-10}

The solution is x=(20ln(3)+7ln(6)+ln(5)-3ln(2))/(ln(3/2))

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5 \cdot 6^{x + 7} = 8 \cdot 9^{x - 10}

x = \frac{20 ln ( 3 ) + 7 ln ( 6 ) + ln ( 5 ) - 3 ln ( 2 )}{ln ( \frac{3}{2} )}

Decimal Notation

x = 83.96421 \dots

Solution steps

5 \cdot 6^{x + 7} = 8 \cdot 9^{x - 10}

Apply exponent rules

ln (5) + (x + 7) ln (6) = ln (8) + (x - 10) ln (9)

Solve

ln (5) + (x + 7) ln (6) = ln (8) + (x - 10) ln (9) : x = \frac{20 ln ( 3 ) + 7 ln ( 6 ) + ln ( 5 ) - 3 ln ( 2 )}{ln ( \frac{3}{2} )}

x = \frac{20 ln ( 3 ) + 7 ln ( 6 ) + ln ( 5 ) - 3 ln ( 2 )}{ln ( \frac{3}{2} )}

x, e^{3 x} = 5

5 \cdot 7^{2 y} = 175

4^{3 x - 2} = 7^{x + 3}

3^{2 x + 1} = 243

x, 93 = 2 3^{x}

What is the answer to 5*6^{x+7}=8*9^{x-10} ?
The answer to 5*6^{x+7}=8*9^{x-10} is x=(20ln(3)+7ln(6)+ln(5)-3ln(2))/(ln(3/2))
Solve for x: 5*6^{x+7}=8*9^{x-10}
The solution is x=(20ln(3)+7ln(6)+ln(5)-3ln(2))/(ln(3/2))