What is simplify-ln(3)-ln(x)-ln(5x) ?

The solution to simplify-ln(3)-ln(x)-ln(5x) is -ln(15x^2)

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simplify-ln(3)-ln(x)-ln(5x)

simplify

- ln (3) - ln (x) - ln (5 x)

- ln (15 x^{2})

Solution steps

- ln (3) - ln (x) - ln (5 x)

Rewrite

- ln (3) - ln (x)

- (ln (3) + ln (x))

= - (ln (x) + ln (3)) - ln (5 x)

Apply log rule:

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

ln (3) + ln (x) = ln (3 x)

= - ln (3 x) - ln (5 x)

Rewrite

- ln (3 x) - ln (5 x)

- (ln (3 x) + ln (5 x))

= - (ln (3 x) + ln (5 x))

Apply log rule:

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

ln (3 x) + ln (5 x) = ln (3 \cdot 5 xx)

= - ln (3 \cdot 5 xx)

Simplify

3 x \cdot 5 x : 15 x^{2}

= - ln (15 x^{2})

- lo g_{2} (\frac{1}{10})

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ln (t x)

What is simplify-ln(3)-ln(x)-ln(5x) ?
The solution to simplify-ln(3)-ln(x)-ln(5x) is -ln(15x^2)