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Popular >

simplify 3ln(2)-2ln(x)+ln(y)

Solution

simplify

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

Solution

ln (\frac{8 y}{x ^{2}})

Solution steps

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

Apply log rule:

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

3 ln (2) = ln (2^{3})

= ln (2^{3}) - 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 (2^{3}) - ln (x^{2}) + ln (y)

Apply log rule:

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

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

= ln (\frac{2 ^{3}}{x ^{2}}) + ln (y)

2^{3} = 8

= ln (\frac{8}{x ^{2}}) + ln (y)

Apply log rule:

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

ln (\frac{8}{x ^{2}}) + ln (y) = ln (\frac{8}{x ^{2}} y)

= ln (\frac{8}{x ^{2}} y)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= ln (\frac{8 y}{x ^{2}})

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Frequently Asked Questions (FAQ)

What is 3ln(2)-2ln(x)+ln(y) ?
The solution to 3ln(2)-2ln(x)+ln(y) is ln((8y)/(x^2))