What is ln(tan(θ))-ln((tan(θ))/5) ?

The solution to ln(tan(θ))-ln((tan(θ))/5) is ln(5)

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simplify ln(tan(θ))-ln((tan(θ))/5)

simplify

ln (tan (θ)) - ln (\frac{tan ( θ )}{5})

ln (5)

Decimal Notation

1.60943 \dots

Solution steps

ln (tan (θ)) - ln (\frac{tan ( θ )}{5})

Apply log rule:

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

ln (tan (θ)) - ln (\frac{tan ( θ )}{5}) = ln (\frac{tan ( θ )}{\frac{t a n ( θ )}{5}})

= ln (\frac{tan ( θ )}{\frac{t a n ( θ )}{5}})

\frac{tan ( θ )}{\frac{t a n ( θ )}{5}} = 5

= ln (5)

5 (lo g_{10} (x y) + lo g_{10} (z))

ln (\frac{x}{9})

ln (\frac{m}{t})

- lo g_{10} (1.58 \cdot 1 0^{- 7})

f (x) = 2 ln (3) - \frac{1}{2} ln (x^{2} + 1)

What is ln(tan(θ))-ln((tan(θ))/5) ?
The solution to ln(tan(θ))-ln((tan(θ))/5) is ln(5)