What is ln(1)-ln(4x)-ln(3x-5) ?

The solution to ln(1)-ln(4x)-ln(3x-5) is -ln(4x(3x-5))

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simplify ln(1)-ln(4x)-ln(3x-5)

simplify

ln (1) - ln (4 x) - ln (3 x - 5)

- ln (4 x (3 x - 5))

Solution steps

ln (1) - ln (4 x) - ln (3 x - 5)

Rewrite

- ln (4 x) - ln (3 x - 5)

- (ln (4 x) + ln (3 x - 5))

= ln (1) - (ln (4 x) + ln (3 x - 5))

Apply log rule:

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

ln (4 x) + ln (3 x - 5) = ln (4 x (3 x - 5))

= ln (1) - ln (4 x (3 x - 5))

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (4 x (3 x - 5))

0 - ln (4 x (3 x - 5)) = - ln (4 x (3 x - 5))

= - ln (4 x (3 x - 5))

2 \cdot 1 0^{l o g_{2} (x) + l o g_{2} (x^{2})}

lo g_{2} (x) + lo g_{2} (3)

\frac{5}{2} ln (\frac{5}{2})

lo g_{10} (x y^{3})

lo g_{10} (z y^{9})

What is ln(1)-ln(4x)-ln(3x-5) ?
The solution to ln(1)-ln(4x)-ln(3x-5) is -ln(4x(3x-5))