What is ln(7)+ln(x)+5ln(y)-2ln(x) ?

The solution to ln(7)+ln(x)+5ln(y)-2ln(x) is ln((7y^5)/x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(7)+ln(x)+5ln(y)-2ln(x)

simplify

ln (7) + ln (x) + 5 ln (y) - 2 ln (x)

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

Solution steps

ln (7) + ln (x) + 5 ln (y) - 2 ln (x)

Apply log rule:

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

ln (7) + ln (x) = ln (7 x)

= ln (7 x) + 5 ln (y) - 2 ln (x)

Apply log rule:

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

5 ln (y) = ln (y^{5})

= ln (7 x) + ln (y^{5}) - 2 ln (x)

Apply log rule:

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

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

= ln (7 x y^{5}) - 2 ln (x)

Apply log rule:

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

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

= ln (7 x y^{5}) - ln (x^{2})

Apply log rule:

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

ln (7 x y^{5}) - ln (x^{2}) = ln (\frac{7 x y ^{5}}{x ^{2}})

= ln (\frac{7 x y ^{5}}{x ^{2}})

Cancel the common factor:

x

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

ln ((x + 5)^{2} \cdot x)

ln (6) - ln (- 9)

ln (\frac{115}{49})

ln (x) + ln (x + 4)

ln (\frac{z ^{4}}{y ^{5}})

What is ln(7)+ln(x)+5ln(y)-2ln(x) ?
The solution to ln(7)+ln(x)+5ln(y)-2ln(x) is ln((7y^5)/x)