What is log_{10}(1/2)+log_{10}(2/3) ?

The solution to log_{10}(1/2)+log_{10}(2/3) is -log_{10}(3)

Popular >

simplify log_{10}(1/2)+log_{10}(2/3)

simplify

lo g_{10} (\frac{1}{2}) + lo g_{10} (\frac{2}{3})

- lo g_{10} (3)

Decimal Notation

- 0.47712 \dots

Solution steps

lo g_{10} (\frac{1}{2}) + lo g_{10} (\frac{2}{3})

Apply log rule:

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

lo g_{10} (\frac{1}{2}) + lo g_{10} (\frac{2}{3}) = lo g_{10} (\frac{1}{2} \cdot \frac{2}{3})

= lo g_{10} (\frac{1}{2} \cdot \frac{2}{3})

Cross-cancel common factor:

2

= lo g_{10} (\frac{1}{3})

\frac{1}{3} = 3^{- 1}

= lo g_{10} (3^{- 1})

Apply log rule:

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

lo g_{10} (3^{- 1}) = - 1 \cdot lo g_{10} (3)

= - 1 \cdot lo g_{10} (3)

Apply rule:

1 \cdot a = a

= - lo g_{10} (3)

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

lo g_{b} (a^{5} b^{4})

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

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

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

What is log_{10}(1/2)+log_{10}(2/3) ?
The solution to log_{10}(1/2)+log_{10}(2/3) is -log_{10}(3)