What is the answer to 1.02^x=2 ?

The answer to 1.02^x=2 is x=(ln(2))/(ln(1.02))

Solve for x: 1.02^x=2

The solution is x=(ln(2))/(ln(1.02))

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1.0 2^{x} = 2

x = \frac{ln ( 2 )}{ln ( 1.02 )}

Decimal Notation

x = 35.00278 \dots

Solution steps

1.0 2^{x} = 2

Apply exponent rules

x ln (1.02) = ln (2)

Solve

x ln (1.02) = ln (2) : x = \frac{ln ( 2 )}{ln ( 1.02 )}

x = \frac{ln ( 2 )}{ln ( 1.02 )}

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

3^{2 x - 3} = 9

7^{2 x + 3} - 8 \cdot 7^{x + 1} + 1 = 0

e^{(l n (0.8)) t} = 0.9

(0.5)^{\frac{9900}{x}} = 0