Question

Suppose log,(7) = a and logo(3) = b. Use the change of base formula along with properties of logarithms to rewrite thefollowing in terms of a and b.- log (9) =help (formulas)log; (3) =help (formulas

Answer 1

Given:

`\log _97=a,\log _93=b`

The change of base formula is,

`\log _b(a)=(\log_xa)/(\log_xb)`

a)

`\begin{gathered} \log _39 \\ \text{Use:}\log _bc=(1)/(\log_cb) \\ \log _39=(1)/(\log_93) \\ \text{Given: }\log _93=b \\ \log _39=(1)/(b) \end{gathered}`

b)

`\begin{gathered} \log _3((7)/(3)) \\ \text{Use:}\log _a(l)/(m)=\log _al-\log _am \\ \log _3((7)/(3))=\log _37-\log _33 \\ We\text{ know, }\log _aa=1 \\ \log _3((7)/(3))=\log _37-1 \\ \log _3((7)/(3))=(\log_97)/(\log_93)-1\ldots\ldots...\text{ Change of base property} \\ \log _3((7)/(3))=(a)/(b)-1 \end{gathered}`

Answer:

`\begin{gathered} \log _39=(1)/(b) \\ \log _3((7)/(3))=(a)/(b)-1 \end{gathered}`