What is the answer to 204.6=0.2((1-2^x)/(1-2)) ?

The answer to 204.6=0.2((1-2^x)/(1-2)) is x=10

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204.6=0.2((1-2^x)/(1-2))

204.6 = 0.2 (\frac{1 - 2 ^{x}}{1 - 2})

x = 10

Solution steps

204.6 = 0.2 (\frac{1 - 2 ^{x}}{1 - 2})

Switch sides

0.2 \cdot \frac{1 - 2 ^{x}}{1 - 2} = 204.6

\frac{1 - 2 ^{x}}{1 - 2} = - (1 - 2^{x})

0.2 (- (- 2^{x} + 1)) = 204.6

Remove parentheses:

(- a) = - a

- 0.2 (1 - 2^{x}) = 204.6

Multiply both sides by

10

- 2 (1 - 2^{x}) = 2046

Divide both sides by

- 2

1 - 2^{x} = - 1023

Move

1

to the right side

- 2^{x} = - 1024

Divide both sides by

- 1

2^{x} = 1024

Apply exponent rules

x = 10

1.02 = 1 - 2 e^{- x} + e^{- 0.5 x}

2 e^{2 x} - 2 = 0

7^{3 x + 4} = 42

t^{2} e^{t} + 2 t e^{t} - 8 e^{t} = 0

ln (\frac{8}{e ^{4 x}}) = 24

What is the answer to 204.6=0.2((1-2^x)/(1-2)) ?
The answer to 204.6=0.2((1-2^x)/(1-2)) is x=10
Solve for x: 204.6=0.2((1-2^x)/(1-2))
The solution is x=10