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Popular >

simplify ln(96)-ln(6)

Solution

simplify

ln (96) - ln (6)

Solution

4 ln (2)

+1

Decimal Notation

2.77258 \dots

Solution steps

ln (96) - ln (6)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (96) - ln (6) = ln (\frac{96}{6})

= ln (\frac{96}{6})

Divide the numbers:

\frac{96}{6} = 16

= ln (16)

Rewrite

16

in power-base form:

16 = 2^{4}

= ln (2^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (2^{4}) = 4 ln (2)

= 4 ln (2)

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Frequently Asked Questions (FAQ)

What is ln(96)-ln(6) ?
The solution to ln(96)-ln(6) is 4ln(2)