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Solve the following logarithm problem for the positive solution for
x.

log_(100)x=-(1)/(2)
Answer:

Solve the following logarithm problem for the positive solution for $x$ . $\newline$ $\log _{100} x=-\frac{1}{2}$ $\newline$ Answer:

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Quotient property of logarithms

Full solution

Q. Solve the following logarithm problem for the positive solution for

x

.

\newline

\log _{100} x=-\frac{1}{2}

\newline

Answer:

Understand the equation: Understand the given logarithmic equation. $\newline$ The equation is $\log_{100}x = -\frac{1}{2}$ , which means we are looking for a number $x$ such that when we take the base $100$ logarithm of $x$ , we get $-\frac{1}{2}$ .
Convert to exponential form: Convert the logarithmic equation to its exponential form. $\newline$ Using the definition of a logarithm, we can rewrite the equation in its exponential form. The base $100$ logarithm of $x$ equals $-(1)/(2)$ means that $100$ raised to the power of $-(1)/(2)$ equals $x$ . $\newline$ So, $100^{-(1)/(2)} = x$ .
Calculate value of $100^{-(1)/(2)}$ : Calculate the value of $100^{-(1)/(2)}$ . $\newline$ The exponent $-(1)/(2)$ is the same as $-0.5$ , which means we are looking for the reciprocal of the square root of $100$ . $\newline$ The square root of $100$ is $10$ , so the reciprocal of $10$ is $1/10$ . $\newline$ Therefore, $100^{-(1)/(2)} = 1/10$ .
Write down solution: Write down the solution for $x$ . From the previous step, we have found that $x$ equals $\frac{1}{10}$ .

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