What is log_{b}(1/10)+log_{b}(40) ?

The solution to log_{b}(1/10)+log_{b}(40) is 2log_{b}(2)

Popular >

simplify log_{b}(1/10)+log_{b}(40)

simplify

lo g_{b} (\frac{1}{10}) + lo g_{b} (40)

2 lo g_{b} (2)

Solution steps

lo g_{b} (\frac{1}{10}) + lo g_{b} (40)

Simplify

lo g_{b} (\frac{1}{10}) : - lo g_{b} (10)

= - lo g_{b} (10) + lo g_{b} (40)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{b} (40) - lo g_{b} (10) = lo g_{b} (\frac{40}{10})

= lo g_{b} (\frac{40}{10})

Divide the numbers:

\frac{40}{10} = 4

= lo g_{b} (4)

Factor the number:

4 = 2^{2}

= lo g_{b} (2^{2})

Apply log rule:

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

lo g_{b} (2^{2}) = 2 lo g_{b} (2)

= 2 lo g_{b} (2)

lo g_{2} (\frac{8}{x + 5})

lo g_{10} (x (x^{2} + 8)^{- \frac{1}{2}})

4 lo g_{10} (2) + lo g_{10} (6) - lo g_{10} (3)

lo g_{4} (\frac{x ^{\frac{7}{2}} y ^{2}}{3 ^{5}})

ln (\frac{7}{8 x ^{8} y})

What is log_{b}(1/10)+log_{b}(40) ?
The solution to log_{b}(1/10)+log_{b}(40) is 2log_{b}(2)