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

The solution to 2ln(5)+2ln(x)-ln(y) is ln((25x^2)/y)

Popular >

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

simplify

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

ln (\frac{25 x ^{2}}{y})

Solution steps

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

Apply log rule:

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

2 ln (5) = ln (5^{2})

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (5^{2}) + ln (x^{2}) = ln (5^{2} x^{2})

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

5^{2} = 25

= ln (25 x^{2}) - ln (y)

Apply log rule:

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

ln (25 x^{2}) - ln (y) = ln (\frac{25 x ^{2}}{y})

= ln (\frac{25 x ^{2}}{y})

ln (\frac{x ^{3} ln ( 2 x )}{e ^{x} sin ( x )})

ln (- i e^{3})

- lo g_{10} (1.2 \cdot 1 0^{- 3})

lo g_{10} (\frac{x ^{4}}{y ^{5}})

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

What is 2ln(5)+2ln(x)-ln(y) ?
The solution to 2ln(5)+2ln(x)-ln(y) is ln((25x^2)/y)