What is 3*log_{10}(a)-2*log_{10}(b)-1 ?

The solution to 3*log_{10}(a)-2*log_{10}(b)-1 is log_{10}((a^3)/(b^2))-1

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simplify 3log_{10}(a)-2log_{10}(b)-1

simplify

3 \cdot lo g_{10} (a) - 2 \cdot lo g_{10} (b) - 1

lo g_{10} (\frac{a ^{3}}{b ^{2}}) - 1

Solution steps

3 lo g_{10} (a) - 2 lo g_{10} (b) - 1

Apply log rule:

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

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

= lo g_{10} (a^{3}) - 2 lo g_{10} (b) - 1

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^{3}) - lo g_{10} (b^{2}) - 1

Apply log rule:

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

lo g_{10} (a^{3}) - lo g_{10} (b^{2}) = lo g_{10} (\frac{a ^{3}}{b ^{2}})

= lo g_{10} (\frac{a ^{3}}{b ^{2}}) - 1

(sin (x) - 1) (ln (sin (x)) - ln (cos (x)))

\frac{5}{9} lo g_{2} (3)

5 lo g_{7} (11) - lo g_{7} (3)

ln (956 \cdot 178108)

- ln (- 2 x)

What is 3*log_{10}(a)-2*log_{10}(b)-1 ?
The solution to 3*log_{10}(a)-2*log_{10}(b)-1 is log_{10}((a^3)/(b^2))-1