en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3ln(4)+ln(2^7)

Solution

simplify

3 ln (4) + ln (2^{7})

Solution

13 ln (2)

+1

Decimal Notation

9.01091 \dots

Solution steps

3 ln (4) + ln (2^{7})

Apply log rule:

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

3 ln (4) = ln (4^{3})

= ln (4^{3}) + ln (2^{7})

Apply log rule:

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

ln (4^{3}) + ln (2^{7}) = ln (2^{7} \cdot 4^{3})

= ln (2^{7} \cdot 4^{3})

4^{3} \cdot 2^{7} = 8192

= ln (8192)

Rewrite

8192

in power-base form:

8192 = 2^{13}

= ln (2^{13})

Apply log rule:

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

ln (2^{13}) = 13 ln (2)

= 13 ln (2)

Popular Examples

simplify 2ln(3^4)+ln(3^3)-ln(9)simplify

2 ln (3^{4}) + ln (3^{3}) - ln (9)

simplify log_{10}((1-p)^x*p)simplify

lo g_{10} ((1 - p)^{x} \cdot p)

simplify ln((1+x)/y)simplify

ln (\frac{1 + x}{y})

simplify 4.76+log_{10}((11)/(4.8))simplify

4.76 + lo g_{10} (\frac{11}{4.8})

simplify ln(x^2sqrt(y))simplify

ln (x^{2} y)

Frequently Asked Questions (FAQ)

What is 3ln(4)+ln(2^7) ?
The solution to 3ln(4)+ln(2^7) is 13ln(2)