What is 2log_{10}(a)+4log_{10}(b)-9log_{10}(c) ?

The solution to 2log_{10}(a)+4log_{10}(b)-9log_{10}(c) is log_{10}((a^2b^4)/(c^9))

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simplify 2log_{10}(a)+4log_{10}(b)-9log_{10}(c)

simplify

2 lo g_{10} (a) + 4 lo g_{10} (b) - 9 lo g_{10} (c)

lo g_{10} (\frac{a ^{2} b ^{4}}{c ^{9}})

Solution steps

2 lo g_{10} (a) + 4 lo g_{10} (b) - 9 lo g_{10} (c)

Apply log rule:

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

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

= lo g_{10} (a^{2}) + 4 lo g_{10} (b) - 9 lo g_{10} (c)

Apply log rule:

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

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

= lo g_{10} (a^{2}) + lo g_{10} (b^{4}) - 9 lo g_{10} (c)

Apply log rule:

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

lo g_{10} (a^{2}) + lo g_{10} (b^{4}) = lo g_{10} (a^{2} b^{4})

= lo g_{10} (a^{2} b^{4}) - 9 lo g_{10} (c)

Apply log rule:

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

9 lo g_{10} (c) = lo g_{10} (c^{9})

= lo g_{10} (a^{2} b^{4}) - lo g_{10} (c^{9})

Apply log rule:

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

lo g_{10} (a^{2} b^{4}) - lo g_{10} (c^{9}) = lo g_{10} (\frac{a ^{2} b ^{4}}{c ^{9}})

= lo g_{10} (\frac{a ^{2} b ^{4}}{c ^{9}})

\frac{1}{2} [5 ln (x + 4) + ln (x) - ln (x^{5} - 3)]

ln (24) - ln (6)

\frac{1}{2} (lo g_{9} (a) + lo g_{9} (b))

2 lo g_{10} (x) + lo g_{10} (6) - lo g_{10} (30)

ln (x) + ln (- ln (x) - ln (4))

What is 2log_{10}(a)+4log_{10}(b)-9log_{10}(c) ?
The solution to 2log_{10}(a)+4log_{10}(b)-9log_{10}(c) is log_{10}((a^2b^4)/(c^9))