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lesson 7.2 - log vs exponent conversions
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7.2 hw - log vs exponent
score: 4.33/19 answered: 3/10
question 4
rewrite the following in logarithmic form:
a) $2^{-2} = \frac{1}{4}$
b) $10^x = 420$
c) $e^5 = x$
note: $\log_{10} \
ightarrow \log$ and $\log_{e} \
ightarrow \ln$
submit question

Explanation:

Part (a)

Step1: Recall the exponential - logarithmic conversion formula

For an exponential equation \(a^{b}=c\), the corresponding logarithmic form is \(\log_{a}c = b\), where \(a>0,a
eq1\).
Here, \(a = 2\), \(b=- 2\) and \(c=\frac{1}{4}\).

Step2: Apply the formula

Using the formula \(\log_{a}c = b\) for \(a = 2\), \(b=-2\) and \(c = \frac{1}{4}\), we get \(\log_{2}\frac{1}{4}=-2\).

Part (b)

Step1: Recall the exponential - logarithmic conversion formula

For an exponential equation \(a^{b}=c\), the corresponding logarithmic form is \(\log_{a}c = b\), where \(a > 0,a
eq1\). Also, when \(a = 10\), we can write \(\log_{10}x=\log x\).
Here, \(a = 10\), \(b = x\) and \(c = 420\).

Step2: Apply the formula

Using the formula \(\log_{a}c=b\) for \(a = 10\), \(b = x\) and \(c=420\), and since \(\log_{10}x=\log x\), we get \(\log420=x\) (or \(\log_{10}420 = x\)).

Part (c)

Step1: Recall the exponential - logarithmic conversion formula for natural logarithm

For an exponential equation \(e^{b}=c\), the corresponding logarithmic form is \(\ln c=b\) (because \(\log_{e}x=\ln x\)).
Here, \(a = e\), \(b = 5\) and \(c=x\).

Step2: Apply the formula

Using the formula \(\ln c=b\) for \(a = e\), \(b = 5\) and \(c = x\), we get \(\ln x=5\).

Answer:

s:
a) \(\log_{2}\frac{1}{4}=-2\)
b) \(\log420 = x\) (or \(\log_{10}420=x\))
c) \(\ln x = 5\)