What is the answer to 3*(2)^{x-1}-2=0 ?

The answer to 3*(2)^{x-1}-2=0 is x=(ln(2/3))/(ln(2))+1

Solve for x: 3*(2)^{x-1}-2=0

The solution is x=(ln(2/3))/(ln(2))+1

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3 \cdot (2)^{x - 1} - 2 = 0

x = \frac{ln ( \frac{2}{3} )}{ln ( 2 )} + 1

Decimal Notation

x = 0.41503 \dots

Solution steps

3 (2)^{x - 1} - 2 = 0

Add

2

to both sides

3 \cdot 2^{x - 1} - 2 + 2 = 0 + 2

Simplify

3 \cdot 2^{x - 1} = 2

Divide both sides by

3

2^{x - 1} = \frac{2}{3}

Apply exponent rules

(x - 1) ln (2) = ln (\frac{2}{3})

Solve

(x - 1) ln (2) = ln (\frac{2}{3}) : x = \frac{ln ( \frac{2}{3} )}{ln ( 2 )} + 1

x = \frac{ln ( \frac{2}{3} )}{ln ( 2 )} + 1

6^{2 x} + 6^{x} - 6 = 0

9 (3^{2 x}) - 22 (3^{x}) - 15 = 0

1 6^{3 x - 6} = 6 4^{x + 4}

2^{2 x + 1} + 3 \cdot 2^{x} - 2 = 0

18 (2^{x}) = 2 + 2^{x + 1}

What is the answer to 3*(2)^{x-1}-2=0 ?
The answer to 3*(2)^{x-1}-2=0 is x=(ln(2/3))/(ln(2))+1
Solve for x: 3*(2)^{x-1}-2=0
The solution is x=(ln(2/3))/(ln(2))+1