What is log_{10}(16)+2log_{10}(3) ?

The solution to log_{10}(16)+2log_{10}(3) is 2log_{10}(12)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{10}(16)+2log_{10}(3)

simplify

lo g_{10} (16) + 2 lo g_{10} (3)

2 lo g_{10} (12)

Decimal Notation

2.15836 \dots

Solution steps

lo g_{10} (16) + 2 lo g_{10} (3)

Apply log rule:

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

2 lo g_{10} (3) = lo g_{10} (3^{2})

= lo g_{10} (16) + lo g_{10} (3^{2})

Apply log rule:

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

lo g_{10} (16) + lo g_{10} (3^{2}) = lo g_{10} (16 \cdot 3^{2})

= lo g_{10} (16 \cdot 3^{2})

16 \cdot 3^{2} = 144

= lo g_{10} (144)

Factor the number:

144 = 1 2^{2}

= lo g_{10} (1 2^{2})

Apply log rule:

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

lo g_{10} (1 2^{2}) = 2 lo g_{10} (12)

= 2 lo g_{10} (12)

ln (\frac{10}{5})

- 4 ln (x) - 5 ln (y) - 8 ln (z)

2 ln (5) - ln (4)

ln (\frac{x}{x ^{2} + 9})

lo g_{5} (k^{2} - 25) - lo g_{5} (k) - 5

What is log_{10}(16)+2log_{10}(3) ?
The solution to log_{10}(16)+2log_{10}(3) is 2log_{10}(12)