What is log_{5}(100)+log_{5}(4) ?

The solution to log_{5}(100)+log_{5}(4) is 2log_{5}(20)

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simplify log_{5}(100)+log_{5}(4)

simplify

lo g_{5} (100) + lo g_{5} (4)

2 lo g_{5} (20)

Decimal Notation

3.72270 \dots

Solution steps

lo g_{5} (100) + lo g_{5} (4)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{5} (100) + lo g_{5} (4) = lo g_{5} (100 \cdot 4)

= lo g_{5} (100 \cdot 4)

Multiply the numbers:

100 \cdot 4 = 400

= lo g_{5} (400)

Factor the number:

400 = 2 0^{2}

= lo g_{5} (2 0^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{5} (2 0^{2}) = 2 lo g_{5} (20)

= 2 lo g_{5} (20)

ln (\frac{s ^{2} + 25}{s ^{2} + 81})

lo g_{a} (\frac{50}{9})

lo g_{10} (\frac{z ^{3}}{x})

2 ln (6) - ln (3)

ln (\frac{2}{7} t^{3})

What is log_{5}(100)+log_{5}(4) ?
The solution to log_{5}(100)+log_{5}(4) is 2log_{5}(20)