What is the answer to 100^n=2 ?

The answer to 100^n=2 is n=(ln(2))/(2ln(10))

The solution is n=(ln(2))/(2ln(10))

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100^n=2

10 0^{n} = 2

n = \frac{ln ( 2 )}{2 ln ( 10 )}

Decimal Notation

n = 0.15051 \dots

Solution steps

10 0^{n} = 2

Apply exponent rules

n ln (100) = ln (2)

Solve

n ln (100) = ln (2) : n = \frac{ln ( 2 )}{2 ln ( 10 )}

n = \frac{ln ( 2 )}{2 ln ( 10 )}

\frac{17}{327} = e^{- 9.22 \cdot 1 0^{- 4} t}

5^{3 x} = 5^{7 x - 2}

2 7^{x - 3} = 8 1^{2 x - 4}

6 e^{4 x - 4} = 42

2 (e^{- x^{2}} - 2 e^{- x^{2}} x^{2}) = 0