What is expand log_{10}((8z)/(11)) ?

The solution to expand log_{10}((8z)/(11)) is 3log_{10}(2)+log_{10}(z)-log_{10}(11)

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expand log_{10}((8z)/(11))

expand

lo g_{10} (\frac{8 z}{11})

3 lo g_{10} (2) + lo g_{10} (z) - lo g_{10} (11)

Solution steps

lo g_{10} (\frac{8 z}{11})

Apply log rule:

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

lo g_{10} (\frac{8 z}{11}) = lo g_{10} (8 z) - lo g_{10} (11)

= lo g_{10} (8 z) - lo g_{10} (11)

Apply log rule:

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

lo g_{10} (8 z) = lo g_{10} (8) + lo g_{10} (z)

= lo g_{10} (8) + lo g_{10} (z) - lo g_{10} (11)

lo g_{10} (8) = 3 lo g_{10} (2)

= 3 lo g_{10} (2) + lo g_{10} (z) - lo g_{10} (11)

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

- lo g_{10} (4.5 \times 1 0^{- 4})

\frac{ln ( \frac{8}{9} )}{2 ln ( 6 )}

ln (x + 8) - ln (x - 8)

ln (e (x))

What is expand log_{10}((8z)/(11)) ?
The solution to expand log_{10}((8z)/(11)) is 3log_{10}(2)+log_{10}(z)-log_{10}(11)