What is ln((4x)/(7y^2)) ?

The solution to ln((4x)/(7y^2)) is 2ln(2)+ln(x)-ln(7)-2ln(y)

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simplify ln((4x)/(7y^2))

simplify

ln (\frac{4 x}{7 y ^{2}})

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

Solution steps

ln (\frac{4 x}{7 y ^{2}})

Apply log rule:

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

ln (\frac{4 x}{7 y ^{2}}) = ln (4 x) - ln (7 y^{2})

= ln (4 x) - ln (7 y^{2})

Apply log rule:

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

ln (4 x) = ln (4) + ln (x), ln (7 y^{2}) = ln (7) + ln (y^{2})

= ln (4) + ln (x) - (ln (y^{2}) + ln (7))

Apply log rule:

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

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

= ln (4) + ln (x) - (ln (7) + 2 ln (y))

ln (4) = 2 ln (2)

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

- (ln (7) + 2 ln (y)) : - ln (7) - 2 ln (y)

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

lo g_{5} (\frac{25 b ^{5} y ^{2} - 6}{y ( x + 6 ) ^{2}})

lo g_{2} (\frac{p ^{5}}{q ^{9}})

- lo g_{10} (6.5 \cdot 1 0^{- 6})

lo g_{10} (\frac{x ^{6}}{z})

2 lo g_{7} (u) + 4 lo g_{7} (v)

What is ln((4x)/(7y^2)) ?
The solution to ln((4x)/(7y^2)) is 2ln(2)+ln(x)-ln(7)-2ln(y)