What is 4log_{10}(a)-1/2 log_{10}(b)+log_{10}(c) ?

The solution to 4log_{10}(a)-1/2 log_{10}(b)+log_{10}(c) is log_{10}((a^4csqrt(b))/b)

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simplify 4log_{10}(a)-1/2 log_{10}(b)+log_{10}(c)

simplify

4 lo g_{10} (a) - \frac{1}{2} lo g_{10} (b) + lo g_{10} (c)

lo g_{10} (\frac{a ^{4} c b}{b})

Solution steps

4 lo g_{10} (a) - \frac{1}{2} lo g_{10} (b) + lo g_{10} (c)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 lo g_{10} (a) = lo g_{10} (a^{4})

= lo g_{10} (a^{4}) - \frac{1}{2} lo g_{10} (b) + lo g_{10} (c)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} lo g_{10} (b) = lo g_{10} (b^{\frac{1}{2}})

= lo g_{10} (a^{4}) - lo g_{10} (b^{\frac{1}{2}}) + lo g_{10} (c)

Apply log rule:

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

lo g_{10} (a^{4}) - lo g_{10} (b^{\frac{1}{2}}) = lo g_{10} (\frac{a ^{4}}{b ^{\frac{1}{2}}})

= lo g_{10} (\frac{a ^{4}}{b ^{\frac{1}{2}}}) + lo g_{10} (c)

Simplify

\frac{a ^{4}}{b ^{\frac{1}{2}}} : \frac{a ^{4} b}{b}

= lo g_{10} (\frac{a ^{4} b}{b}) + lo g_{10} (c)

Apply log rule:

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

lo g_{10} (\frac{a ^{4} b}{b}) + lo g_{10} (c) = lo g_{10} (\frac{a ^{4} b}{b} c)

= lo g_{10} (\frac{a ^{4} b}{b} c)

Simplify

\frac{a ^{4} b}{b} c : \frac{a ^{4} c b}{b}

= lo g_{10} (\frac{a ^{4} c b}{b})

ln (e^{19} x^{20})

lo g_{10} (\frac{x ^{3} ( x + 3 )}{( x - 1 ) x + 5})

\frac{2 ln ( 2 )}{ln ( 2 ) - 2 ln ( 3 )}

- \frac{1}{ln ( 10 ) 0.5 \cdot lo g _{10} ( 0. 5 ^{2} )} - \frac{7}{( 0 , 5 + 3 ) ^{3}}

lo g_{3} (\frac{m}{n})

What is 4log_{10}(a)-1/2 log_{10}(b)+log_{10}(c) ?
The solution to 4log_{10}(a)-1/2 log_{10}(b)+log_{10}(c) is log_{10}((a^4csqrt(b))/b)