What is ln(sin(θ))-ln((sin(θ))/6) ?

The solution to ln(sin(θ))-ln((sin(θ))/6) is ln(6)

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simplify ln(sin(θ))-ln((sin(θ))/6)

simplify

ln (sin (θ)) - ln (\frac{sin ( θ )}{6})

ln (6)

Decimal Notation

1.79175 \dots

Solution steps

ln (sin (θ)) - ln (\frac{sin ( θ )}{6})

Apply log rule:

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

ln (sin (θ)) - ln (\frac{sin ( θ )}{6}) = ln (\frac{sin ( θ )}{\frac{s i n ( θ )}{6}})

= ln (\frac{sin ( θ )}{\frac{s i n ( θ )}{6}})

\frac{sin ( θ )}{\frac{s i n ( θ )}{6}} = 6

= ln (6)

lo g_{10} (x) - 3 lo g_{10} (y) - 2 lo g_{10} (z)

\frac{1}{3} lo g_{10} (x) + 2 lo g_{10} (y)

lo g_{6} (5 z)

lo g_{6} (5 x)

lo g_{8} (\frac{w ^{4} x ^{2}}{yz})

What is ln(sin(θ))-ln((sin(θ))/6) ?
The solution to ln(sin(θ))-ln((sin(θ))/6) is ln(6)