What is log_{5}(2)+log_{5}(20)-log_{5}(4) ?

The solution to log_{5}(2)+log_{5}(20)-log_{5}(4) is log_{5}(10)

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simplify log_{5}(2)+log_{5}(20)-log_{5}(4)

simplify

lo g_{5} (2) + lo g_{5} (20) - lo g_{5} (4)

lo g_{5} (10)

Decimal Notation

1.43067 \dots

Solution steps

lo g_{5} (2) + lo g_{5} (20) - lo g_{5} (4)

Apply log rule:

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

lo g_{5} (2) + lo g_{5} (20) = lo g_{5} (2 \cdot 20)

= lo g_{5} (2 \cdot 20) - lo g_{5} (4)

Multiply the numbers:

2 \cdot 20 = 40

= lo g_{5} (40) - lo g_{5} (4)

Apply log rule:

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

lo g_{5} (40) - lo g_{5} (4) = lo g_{5} (\frac{40}{4})

= lo g_{5} (\frac{40}{4})

Divide the numbers:

\frac{40}{4} = 10

= lo g_{5} (10)

ln ∣ z + 4 ∣ + \frac{6}{5} ln ∣ z - 1 ∣ - \frac{6}{5} ln ∣ z + 4 ∣ + ln ∣ x ∣

\frac{1}{2} ln ∣ 2 (10.3) + 1 ∣ + 2 ln ∣ (10.3) - 1 ∣

\frac{1}{4} ln (\frac{3 e ^{\frac{3}{2} x}}{3 e ^{\frac{3}{2} x} - 2})

ln (\frac{2.3}{2.6})

\frac{1}{2} [ln (x + 1) + 2 ln (x - 1)] + 3 ln (x)

What is log_{5}(2)+log_{5}(20)-log_{5}(4) ?
The solution to log_{5}(2)+log_{5}(20)-log_{5}(4) is log_{5}(10)