What is 13log_{10}(a)-2log_{10}(b)+log_{10}(c) ?

The solution to 13log_{10}(a)-2log_{10}(b)+log_{10}(c) is log_{10}((a^{13}c)/(b^2))

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simplify 13log_{10}(a)-2log_{10}(b)+log_{10}(c)

simplify

13 lo g_{10} (a) - 2 lo g_{10} (b) + lo g_{10} (c)

lo g_{10} (\frac{a ^{13} c}{b ^{2}})

Solution steps

13 lo g_{10} (a) - 2 lo g_{10} (b) + lo g_{10} (c)

Apply log rule:

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

13 lo g_{10} (a) = lo g_{10} (a^{13})

= lo g_{10} (a^{13}) - 2 lo g_{10} (b) + lo g_{10} (c)

Apply log rule:

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

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

= lo g_{10} (a^{13}) - lo g_{10} (b^{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^{13}) - lo g_{10} (b^{2}) = lo g_{10} (\frac{a ^{13}}{b ^{2}})

= lo g_{10} (\frac{a ^{13}}{b ^{2}}) + lo g_{10} (c)

Apply log rule:

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

lo g_{10} (\frac{a ^{13}}{b ^{2}}) + lo g_{10} (c) = lo g_{10} (\frac{a ^{13}}{b ^{2}} c)

= lo g_{10} (\frac{a ^{13}}{b ^{2}} c)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{10} (\frac{a ^{13} c}{b ^{2}})

ln (4) + 2 ln (4^{2} + 4) - ln (1) + 2 ln (1^{2} + 4)

2 ln (2) + \frac{17 ln ( 2 ) - 9 ln ( 3 )}{5}

ln (x) - ln (x^{3})

lo g_{2} (\frac{6 x ^{2}}{y z ^{3}})

ln (\frac{ln ( e - x )}{x})

What is 13log_{10}(a)-2log_{10}(b)+log_{10}(c) ?
The solution to 13log_{10}(a)-2log_{10}(b)+log_{10}(c) is log_{10}((a^{13}c)/(b^2))