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lesson 7.2 - log vs exponent conversions
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7.2 hw - log vs exponent
score: 15.33/19 answered: 8/10
question 9
solve for ( x ). give answer as a reduced and simplified fraction if needed.
( log_{5}(x) = -3 )
( x = )

Explanation:

Step1: Recall log to exponent conversion

The logarithmic equation $\log_{b}(a) = c$ is equivalent to the exponential equation $b^{c}=a$.

Step2: Apply the conversion to given equation

For the equation $\log_{5}(x)= - 3$, using the conversion formula with $b = 5$, $c=-3$ and $a = x$, we get $5^{-3}=x$.

Step3: Simplify the exponential expression

We know that $a^{-n}=\frac{1}{a^{n}}$, so $5^{-3}=\frac{1}{5^{3}}$. And $5^{3}=5\times5\times5 = 125$. So $x=\frac{1}{125}$.

Answer:

$\frac{1}{125}$