Question

lesson 7.2 - log vs exponent conversions
completed notes (coming soon)
video tutorial
7.2 hw - log vs exponent
score: 0/19 answered: 0/10
question 1
rewrite the following in logarithmic form:
a) $3^2 = 9$
b) $10^x = 168$
c) $e^0 = x$
note: $log_{10} \
ightarrow \log$ and $log_{e} \
ightarrow \ln$

Explanation:

Part (a)

Step1: Recall the exponential - logarithmic conversion formula

The general formula for converting an exponential equation \(a^{b}=c\) (where \(a>0,a
eq1\)) to logarithmic form is \(\log_{a}c = b\).
For the equation \(3^{2}=9\), we have \(a = 3\), \(b = 2\) and \(c=9\).

Step2: Apply the formula

Using the formula \(\log_{a}c=b\) with \(a = 3\), \(b = 2\) and \(c = 9\), we get \(\log_{3}9=2\).

Part (b)

Step1: Recall the exponential - logarithmic conversion formula and the note

The general formula for converting an exponential equation \(a^{b}=c\) (where \(a>0,a
eq1\)) to logarithmic form is \(\log_{a}c = b\). Also, from the note, \(\log_{10}\) is written as \(\log\).
For the equation \(10^{x}=168\), we have \(a = 10\), \(b=x\) and \(c = 168\).

Step2: Apply the formula

Using the formula \(\log_{a}c=b\) with \(a = 10\), \(b = x\) and \(c=168\), and using the note that \(\log_{10}\) is \(\log\), we get \(\log(168)=x\) (or \(\log_{10}168=x\)).

Part (c)

Step1: Recall the exponential - logarithmic conversion formula and the note

The general formula for converting an exponential equation \(a^{b}=c\) (where \(a>0,a
eq1\)) to logarithmic form is \(\log_{a}c = b\). Also, from the note, \(\log_{e}\) is written as \(\ln\).
For the equation \(e^{0}=x\), we have \(a = e\), \(b = 0\) and \(c=x\).

Step2: Apply the formula

Using the formula \(\log_{a}c=b\) with \(a = e\), \(b = 0\) and \(c=x\), and using the note that \(\log_{e}\) is \(\ln\), we get \(\ln(x)=0\) (or \(\log_{e}x = 0\)).

Answer:

s:
a) \(\log_{3}9 = 2\)

b) \(\log(168)=x\) (or \(\log_{10}168=x\))

c) \(\ln(x)=0\) (or \(\log_{e}x = 0\))