Question

Fill in the missing values to make the equations true.(a) log, 9-log, 11 = log5(b) log45 + log4 = log, 45(c) 5log72 = log7

Answer 1

(a)

`\log _59-\log _511=\log _{5_{}}((9)/(11))\text{ (}\because\log a-\log b=\log ((a)/(b))`

Thus, the required value in the blank in 9/11/

(b)

`\log _45+\log _4(9)=\log _445\text{ (}\because\log a+\log b=\log ab)`

Thus, the required value in the blank is 9.

(c)

`\begin{gathered} 5\log _72=\log _72^5(\because a\log b=\log b^a) \\ =\log _732 \end{gathered}`

Thus, the requried value in the blank is 32.