What is the answer to 2=100^x ?

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

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

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2=100^x

2 = 10 0^{x}

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

Decimal

x = 0.15051 \dots

Solution steps

2 = 10 0^{x}

Apply exponent rules

ln (2) = x ln (100)

Solve

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

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

3^{x} + 3^{x - 1} + 3^{x + 1} = 117

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

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

200000 = 700 (2)^{\frac{t}{30}}

102 4^{x + 1} = 1 6^{3 x + 4}