What is log_{10}(4)+log_{10}(8) ?

The solution to log_{10}(4)+log_{10}(8) is 5log_{10}(2)

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simplify log_{10}(4)+log_{10}(8)

simplify

lo g_{10} (4) + lo g_{10} (8)

5 lo g_{10} (2)

Decimal Notation

1.50514 \dots

Solution steps

lo g_{10} (4) + lo g_{10} (8)

Apply log rule:

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

lo g_{10} (4) + lo g_{10} (8) = lo g_{10} (4 \cdot 8)

= lo g_{10} (4 \cdot 8)

Multiply the numbers:

4 \cdot 8 = 32

= lo g_{10} (32)

Factor the number:

32 = 2^{5}

= lo g_{10} (2^{5})

Apply log rule:

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

lo g_{10} (2^{5}) = 5 lo g_{10} (2)

= 5 lo g_{10} (2)

lo g_{10} (4) + lo g_{10} (5) + lo g_{10} (3)

lo g_{2} (2 x) - lo g_{2} (x + 1)

ln (\frac{e}{4})

lo g_{m} (m x^{2})

ln (2) + x ln (x) + x - 2 ln (x - 1) - 3

What is log_{10}(4)+log_{10}(8) ?
The solution to log_{10}(4)+log_{10}(8) is 5log_{10}(2)