What is the answer to solvefor x,5e^{2-x}=10^{x+4} ?

The answer to solvefor x,5e^{2-x}=10^{x+4} is x=(ln(2000)-2)/(-1-ln(10))

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solvefor x,5e^{2-x}=10^{x+4}

solve for

x, 5 e^{2 - x} = 1 0^{x + 4}

x = \frac{ln ( 2000 ) - 2}{- 1 - ln ( 10 )}

Decimal Notation

x = - 1.69591 \dots

Solution steps

5 e^{2 - x} = 1 0^{x + 4}

Apply exponent rules

ln (5) + 2 - x = (x + 4) ln (10)

Solve

ln (5) + 2 - x = (x + 4) ln (10) : x = \frac{ln ( 2000 ) - 2}{- 1 - ln ( 10 )}

x = \frac{ln ( 2000 ) - 2}{- 1 - ln ( 10 )}

12 5^{x - 2} = 25

8 \cdot 3^{x + 1} + 3^{x + 1} = 1

24 \cdot 2^{- 0.014 x} = 6

5^{x + 2} = 5^{6}

5^{x + 2} = 5^{9}

What is the answer to solvefor x,5e^{2-x}=10^{x+4} ?
The answer to solvefor x,5e^{2-x}=10^{x+4} is x=(ln(2000)-2)/(-1-ln(10))