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Popular >

simplify 3ln(2)+ln(5)-ln(4)

Solution

simplify

3 ln (2) + ln (5) - ln (4)

Solution

ln (10)

+1

Decimal Notation

2.30258 \dots

Solution steps

3 ln (2) + ln (5) - ln (4)

Apply log rule:

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

3 ln (2) = ln (2^{3})

= ln (2^{3}) + ln (5) - ln (4)

Apply log rule:

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

ln (2^{3}) + ln (5) = ln (2^{3} \cdot 5)

= ln (2^{3} \cdot 5) - ln (4)

2^{3} \cdot 5 = 40

= ln (40) - ln (4)

Apply log rule:

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

ln (40) - ln (4) = ln (\frac{40}{4})

= ln (\frac{40}{4})

Divide the numbers:

\frac{40}{4} = 10

= ln (10)

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Frequently Asked Questions (FAQ)

What is 3ln(2)+ln(5)-ln(4) ?
The solution to 3ln(2)+ln(5)-ln(4) is ln(10)