Rewrite the expression as a single logarithm.5*1n(r)+3*1n(t)-4*1n(s)

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Paulina Horne · Accepted Answer

Remember   log  ⁡  (  a      /    b  )  =  log  ⁡  (  a  )  −  log  ⁡  (  b  )  log  ⁡  (  a  .  b  )  =  log  ⁡  (  a  )  +  log  ⁡  (  b  )  log  ⁡  (      a          n        )  =  n  .  log  ⁡  (  a  )  =  ln  ⁡  (      r          5        )  +  ln  ⁡  (      t          3        )  −  ln  ⁡  (      s          4        )  =  ln  ⁡  (      r          5        ∗      t          3        )  −  ln  ⁡  (      s          4        )  =  ln

proximumha · Accepted Answer

Rewrite the expression as a single logarithm.
5*1n(r)+3*1n(t)-4*1n(s)
Use the law of logarithm:

\log_{a} (A^{C}) = C \log_{a} A

, to get exponents.

= \ln (r)^{5} + \ln (t)^{3} - \ln (s)^{4}

Next, use the law of logarithm:

\log_{a} (A B) = \log_{a} A + \log_{a} B

= \ln (r^{5} t^{3}) - \ln (s)^{4}

Finally, use the law of logarithm:

\log_{a} (\frac{A}{B}) = \log_{a} A - \log_{a} B

= \ln (\frac{r^{5} t^{3}}{s^{4}})

(answer)

Rewrite the expression as a single logarithm. 51n(r)+31n(t)-4*1n(s)

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