What is 2-log_{5}(1/16)-1/3 log_{5}(8) ?

The solution to 2-log_{5}(1/16)-1/3 log_{5}(8) is 2+3log_{5}(2)

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simplify 2-log_{5}(1/16)-1/3 log_{5}(8)

simplify

2 - lo g_{5} (\frac{1}{16}) - \frac{1}{3} lo g_{5} (8)

2 + 3 lo g_{5} (2)

Decimal Notation

3.29202 \dots

Solution steps

2 - lo g_{5} (\frac{1}{16}) - \frac{1}{3} lo g_{5} (8)

lo g_{5} (\frac{1}{16}) = - 4 lo g_{5} (2)

\frac{1}{3} lo g_{5} (8) = lo g_{5} (2)

= 2 - (- 4 lo g_{5} (2)) - lo g_{5} (2)

Apply rule:

a - (- b) = a + b

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

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

Add similar elements:

4 lo g_{5} (2) - lo g_{5} (2) = 3 lo g_{5} (2)

= 2 + 3 lo g_{5} (2)

5 ln (x) + 4 ln (y) - 2 ln (z)

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

4 ln (2) - \frac{1}{2} ln (25)

10 lo g_{10} (\frac{S}{1 0 ^{- 12}})

ln (\frac{67}{150})

What is 2-log_{5}(1/16)-1/3 log_{5}(8) ?
The solution to 2-log_{5}(1/16)-1/3 log_{5}(8) is 2+3log_{5}(2)