What is the answer to 0.2e^{4x}-0.1e^{-3x}=0 ?

The answer to 0.2e^{4x}-0.1e^{-3x}=0 is x=(ln(0.1)-ln(0.2))/7

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0.2e^{4x}-0.1e^{-3x}=0

0.2 e^{4 x} - 0.1 e^{- 3 x} = 0

x = \frac{ln ( 0.1 ) - ln ( 0.2 )}{7}

Decimal Notation

x = - 0.09902 \dots

Solution steps

0.2 e^{4 x} - 0.1 e^{- 3 x} = 0

Add

0.1 e^{- 3 x}

to both sides

0.2 e^{4 x} - 0.1 e^{- 3 x} + 0.1 e^{- 3 x} = 0 + 0.1 e^{- 3 x}

Simplify

0.2 e^{4 x} = 0.1 e^{- 3 x}

Apply exponent rules

ln (0.2) + 4 x = ln (0.1) - 3 x

Solve

ln (0.2) + 4 x = ln (0.1) - 3 x : x = \frac{ln ( 0.1 ) - ln ( 0.2 )}{7}

x = \frac{ln ( 0.1 ) - ln ( 0.2 )}{7}

(1 4^{3 x + 1}) (8^{2 x + 3}) = 7

5^{x} = 22

5^{x} = 23

5^{x} = 14

5^{x} = - 1

What is the answer to 0.2e^{4x}-0.1e^{-3x}=0 ?
The answer to 0.2e^{4x}-0.1e^{-3x}=0 is x=(ln(0.1)-ln(0.2))/7