What is the answer to 38.5^x=6.5^{(x-2)} ?

The answer to 38.5^x=6.5^{(x-2)} is x=-(2ln(6.5))/(ln(38.5)-ln(6.5))

Solve for x: 38.5^x=6.5^{(x-2)}

The solution is x=-(2ln(6.5))/(ln(38.5)-ln(6.5))

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38. 5^{x} = 6. 5^{(x - 2)}

x = - \frac{2 ln ( 6.5 )}{ln ( 38.5 ) - ln ( 6.5 )}

Decimal Notation

x = - 2.10450 \dots

Solution steps

38. 5^{x} = 6. 5^{(x - 2)}

Apply exponent rules

x ln (38.5) = (x - 2) ln (6.5)

Solve

x ln (38.5) = (x - 2) ln (6.5) : x = - \frac{2 ln ( 6.5 )}{ln ( 38.5 ) - ln ( 6.5 )}

x = - \frac{2 ln ( 6.5 )}{ln ( 38.5 ) - ln ( 6.5 )}

(- 2)^{3^{2}} - (- 2)^{2^{x}} = 0

3^{2 (x - 1)} = 2^{x - 3}

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

51 e^{x} = 510

9^{x + 3} = 24 3^{3 - x}

What is the answer to 38.5^x=6.5^{(x-2)} ?
The answer to 38.5^x=6.5^{(x-2)} is x=-(2ln(6.5))/(ln(38.5)-ln(6.5))
Solve for x: 38.5^x=6.5^{(x-2)}
The solution is x=-(2ln(6.5))/(ln(38.5)-ln(6.5))