en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((5x^7)/y)

Solution

simplify

ln (\frac{5 x ^{7}}{y})

Solution

ln (5) + 7 ln (x) - ln (y)

Solution steps

ln (\frac{5 x ^{7}}{y})

Apply log rule:

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

ln (\frac{5 x ^{7}}{y}) = ln (5 x^{7}) - ln (y)

= ln (5 x^{7}) - ln (y)

Apply log rule:

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

ln (5 x^{7}) = ln (5) + ln (x^{7})

= ln (5) + ln (x^{7}) - ln (y)

Apply log rule:

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

ln (x^{7}) = 7 ln (x)

= ln (5) + 7 ln (x) - ln (y)

Popular Examples

simplify 3*ln(5)-3*ln(2)simplify

3 \cdot ln (5) - 3 \cdot ln (2)

expand log_{e}((6x^2)/(y^4))expand

lo g_{e} (\frac{6 x ^{2}}{y ^{4}})

simplify 0.0259*ln((4*10^{15})/(1.5*10^{10)})simplify

0.0259 \cdot ln (\frac{4 \cdot 1 0 ^{15}}{1.5 \cdot 1 0 ^{10}})

simplify ln(((\frac{0.302)/(0.303))}{9.9})simplify

ln (\frac{( \frac{0.302}{0.303} )}{9.9})

simplify ln(e^xx^2)simplify

ln (e^{x} x^{2})

Frequently Asked Questions (FAQ)

What is ln((5x^7)/y) ?
The solution to ln((5x^7)/y) is ln(5)+7ln(x)-ln(y)