What is log_{d}(sqrt(a))+9log_{d}(b)-3log_{d}(c) ?

The solution to log_{d}(sqrt(a))+9log_{d}(b)-3log_{d}(c) is log_{d}((sqrt(a)b^9)/(c^3))

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simplify log_{d}(sqrt(a))+9log_{d}(b)-3log_{d}(c)

simplify

lo g_{d} (a) + 9 lo g_{d} (b) - 3 lo g_{d} (c)

lo g_{d} (\frac{a b ^{9}}{c ^{3}})

Solution steps

lo g_{d} (a) + 9 lo g_{d} (b) - 3 lo g_{d} (c)

Apply log rule:

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

9 lo g_{d} (b) = lo g_{d} (b^{9})

= lo g_{d} (a) + lo g_{d} (b^{9}) - 3 lo g_{d} (c)

Apply log rule:

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

lo g_{d} (a) + lo g_{d} (b^{9}) = lo g_{d} (b^{9} a)

= lo g_{d} (a b^{9}) - 3 lo g_{d} (c)

Apply log rule:

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

3 lo g_{d} (c) = lo g_{d} (c^{3})

= lo g_{d} (b^{9} a) - lo g_{d} (c^{3})

Apply log rule:

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

lo g_{d} (b^{9} a) - lo g_{d} (c^{3}) = lo g_{d} (\frac{b ^{9} a}{c ^{3}})

= lo g_{d} (\frac{a b ^{9}}{c ^{3}})

- ln (\frac{x}{4})

4.57 - lo g_{10} (\frac{0.049}{0.21})

ln (\cdot 4 x)

3 ln (t - 2) - 3 ln (t - 1)

- 2 ln (ln (x)) - ln (x)

What is log_{d}(sqrt(a))+9log_{d}(b)-3log_{d}(c) ?
The solution to log_{d}(sqrt(a))+9log_{d}(b)-3log_{d}(c) is log_{d}((sqrt(a)b^9)/(c^3))