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Popular >

simplify ln(8)-2ln(4)+ln(15)

Solution

simplify

ln (8) - 2 ln (4) + ln (15)

Solution

ln (\frac{15}{2})

+1

Decimal Notation

2.01490 \dots

Solution steps

ln (8) - 2 ln (4) + ln (15)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (8) - ln (4^{2}) + ln (15)

Apply log rule:

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

ln (8) - ln (4^{2}) = ln (\frac{8}{4 ^{2}})

= ln (\frac{8}{4 ^{2}}) + ln (15)

\frac{8}{4 ^{2}} = \frac{1}{2}

= ln (\frac{1}{2}) + ln (15)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{1}{2}) + ln (15) = ln (15 \cdot \frac{1}{2})

= ln (15 \cdot \frac{1}{2})

\frac{1}{2} \cdot 15 = \frac{15}{2}

= ln (\frac{15}{2})

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Frequently Asked Questions (FAQ)

What is ln(8)-2ln(4)+ln(15) ?
The solution to ln(8)-2ln(4)+ln(15) is ln(15/2)