Question

lesson 7.2 - log vs exponent conversions
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7.2 hw - log vs exponent
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question 2
rewrite the following in exponential form

a) \\(\log_{4}\left(\frac{1}{16}\
ight) = -2\\)

b) \\(\log(338) = x\\)

c) \\(\ln(x) = 4\\)
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Explanation:

Part a)

Step1: Recall log to exponent rule

The logarithmic equation $\log_b(a) = c$ converts to exponential form as $b^c = a$. Here, $b = 4$, $a=\frac{1}{16}$, $c=-2$.

Step2: Apply the rule

Substitute into the formula: $4^{-2}=\frac{1}{16}$.

Part b)

Step1: Recall log (base 10) to exponent rule

For $\log(a)=x$ (where base is 10, since it's common log), the rule $\log_b(a) = c\implies b^c = a$ applies with $b = 10$, $a = 338$, $c = x$.

Step2: Apply the rule

We get $10^x = 338$.

Part c)

Step1: Recall natural log (ln) to exponent rule

$\ln(x)=4$ means $\log_e(x)=4$ (since $\ln$ is log base $e$). Using $\log_b(a) = c\implies b^c = a$ with $b = e$, $a = x$, $c = 4$.

Step2: Apply the rule

We get $e^4 = x$.

Answer:

a) $4^{-2}=\frac{1}{16}$
b) $10^x = 338$
c) $e^4 = x$