en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3ln(3)-3ln(1/2)

Solution

simplify

3 ln (3) - 3 ln (\frac{1}{2})

Solution

3 ln (6)

+1

Solution steps

3 ln (3) - 3 ln (\frac{1}{2})

Apply log rule:

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

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

= ln (3^{3}) - 3 ln (\frac{1}{2})

Apply log rule:

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

3 ln (\frac{1}{2}) = ln ((\frac{1}{2})^{3})

= ln (3^{3}) - ln ((\frac{1}{2})^{3})

Apply log rule:

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

ln (3^{3}) - ln ((\frac{1}{2})^{3}) = ln (\frac{3 ^{3}}{( \frac{1}{2} ) ^{3}})

= ln (\frac{3 ^{3}}{( \frac{1}{2} ) ^{3}})

\frac{3 ^{3}}{( \frac{1}{2} ) ^{3}} = 216

= ln (216)

Rewrite

216

in power-base form:

216 = 6^{3}

= ln (6^{3})

Apply log rule:

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

ln (6^{3}) = 3 ln (6)

= 3 ln (6)

Popular Examples

simplify ln(1/2)+1 simplify

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

simplify ln(7sec(θ))+ln(4cos(θ))simplify

ln (7 sec (θ)) + ln (4 cos (θ))

simplify ln(d+l)-ln(d)simplify

ln (d + l) - ln (d)

simplify ln(a)-(2ln(b)-ln(c))simplify

ln (a) - (2 ln (b) - ln (c))

simplify ln(Ae^2)simplify

ln (A e^{2})

Frequently Asked Questions (FAQ)

What is 3ln(3)-3ln(1/2) ?
The solution to 3ln(3)-3ln(1/2) is 3ln(6)