What is the answer to 1.03^x=2 ?

The answer to 1.03^x=2 is x=(ln(2))/(ln(1.03))

Solve for x: 1.03^x=2

The solution is x=(ln(2))/(ln(1.03))

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1.0 3^{x} = 2

x = \frac{ln ( 2 )}{ln ( 1.03 )}

Decimal Notation

x = 23.44977 \dots

Solution steps

1.0 3^{x} = 2

Apply exponent rules

x ln (1.03) = ln (2)

Solve

x ln (1.03) = ln (2) : x = \frac{ln ( 2 )}{ln ( 1.03 )}

x = \frac{ln ( 2 )}{ln ( 1.03 )}

4^{x} + 4^{2} = 4^{x + 2}

4^{x} + 48 = 19 \cdot 2^{x}

64 (4^{2 x}) - 20 (4^{x}) + 1 = 0

3 \cdot 9^{x} - 10 \cdot 3^{x} + 3 = 0

6^{x} = 23