What is the answer to 5*10^{2x}=1 ?

The answer to 5*10^{2x}=1 is x=-(ln(5))/(2ln(10))

Solve for x: 5*10^{2x}=1

The solution is x=-(ln(5))/(2ln(10))

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5 \cdot 1 0^{2 x} = 1

x = - \frac{ln ( 5 )}{2 ln ( 10 )}

Decimal Notation

x = - 0.34948 \dots

Solution steps

5 \cdot 1 0^{2 x} = 1

Divide both sides by

5

1 0^{2 x} = \frac{1}{5}

Apply exponent rules

2 x ln (10) = ln (\frac{1}{5})

Solve

2 x ln (10) = ln (\frac{1}{5}) : x = - \frac{ln ( 5 )}{2 ln ( 10 )}

x = - \frac{ln ( 5 )}{2 ln ( 10 )}

4^{2 x + 7} = 3 2^{2 x - 3}

(5^{x})^{- 1} = 25

32 = 2^{x - 3}

\frac{1}{16} = 2^{x}

1 0^{5 x} = 8

What is the answer to 5*10^{2x}=1 ?
The answer to 5*10^{2x}=1 is x=-(ln(5))/(2ln(10))
Solve for x: 5*10^{2x}=1
The solution is x=-(ln(5))/(2ln(10))