What is 0.33*log_{10}(0.33)+0.67*log_{10}(0.67) ?

The solution to 0.33*log_{10}(0.33)+0.67*log_{10}(0.67) is log_{10}(67^{0.67}*33^{0.33})-2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 0.33log_{10}(0.33)+0.67log_{10}(0.67)

simplify

0.33 \cdot lo g_{10} (0.33) + 0.67 \cdot lo g_{10} (0.67)

lo g_{10} (6 7^{0.67} \cdot 3 3^{0.33}) - 2

Decimal Notation

- 0.27542 \dots

Solution steps

0.33 lo g_{10} (0.33) + 0.67 lo g_{10} (0.67)

0.33 lo g_{10} (0.33) = 0.33 lo g_{10} (\frac{33}{100})

0.67 lo g_{10} (0.67) = 0.67 lo g_{10} (\frac{67}{100})

= 0.33 lo g_{10} (\frac{33}{100}) + 0.67 lo g_{10} (\frac{67}{100})

0.33 lo g_{10} (\frac{33}{100}) = lo g_{10} ((\frac{33}{100})^{0.33})

0.67 lo g_{10} (\frac{67}{100}) = lo g_{10} ((\frac{67}{100})^{0.67})

= lo g_{10} ((\frac{33}{100})^{0.33}) + lo g_{10} ((\frac{67}{100})^{0.67})

Apply log rule:

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

lo g_{10} ((\frac{33}{100})^{0.33}) + lo g_{10} ((\frac{67}{100})^{0.67}) = lo g_{10} ((\frac{33}{100})^{0.33} (\frac{67}{100})^{0.67})

= lo g_{10} ((\frac{33}{100})^{0.33} (\frac{67}{100})^{0.67})

Simplify

(\frac{33}{100})^{0.33} (\frac{67}{100})^{0.67} : \frac{3 3 ^{0.33} \cdot 6 7 ^{0.67}}{100}

= lo g_{10} (\frac{3 3 ^{0.33} \cdot 6 7 ^{0.67}}{100})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{3 3 ^{0.33} \cdot 6 7 ^{0.67}}{100}) = lo g_{10} (3 3^{0.33} \cdot 6 7^{0.67}) - lo g_{10} (100)

= lo g_{10} (3 3^{0.33} \cdot 6 7^{0.67}) - lo g_{10} (100)

Simplify

lo g_{10} (100) : 2

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (3 3^{0.33} \cdot 6 7^{0.67}) = lo g_{10} (6 7^{0.67}) + lo g_{10} (3 3^{0.33})

= lo g_{10} (6 7^{0.67}) + lo g_{10} (3 3^{0.33}) - 2

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (6 7^{0.67}) + lo g_{10} (3 3^{0.33}) = lo g_{10} (6 7^{0.67} \cdot 3 3^{0.33})

= lo g_{10} (6 7^{0.67} \cdot 3 3^{0.33}) - 2

ln (x) + ln (x) + 3 ln (3 x)

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

ln (a - b) + ln (a + b)

ln v + v^{2} - ln ∣ v ∣

ln (\frac{15000}{15})

What is 0.33*log_{10}(0.33)+0.67*log_{10}(0.67) ?
The solution to 0.33*log_{10}(0.33)+0.67*log_{10}(0.67) is log_{10}(67^{0.67}*33^{0.33})-2