Question

If log a=4 log b= -16 and log c=19 find value of log a^2c (——-) /—— / B

Answer 1

We have the following

`\begin{gathered} \log a=4 \\ \log b=-16 \\ \log c=19 \\ \log (\frac{a^2\cdot c}{\sqrt[]{b}}) \end{gathered}`

Let's find a, b and c in order to solve the problem

a.

`\begin{gathered} \log a=4 \\ a=10^4=10000 \end{gathered}`

a = 10,000

b.

`\begin{gathered} \log b=-16 \\ b=10^(-16)=(1)/(10^(16)) \end{gathered}`

b=1.0E-16

c.

`\begin{gathered} \log c=19 \\ c=10^(19) \end{gathered}`

c=1.0E19

Thus, the value of log [ a^2c/sqrt(c) ] is :

replace:

`\log (\frac{a^2\cdot c}{\sqrt[]{b}})=\log _(10)\mleft(\frac{\left(10^4\right)^2\cdot\:10^(19)}{\sqrt{10^(-16)}}\mright)`

simplify:

`\begin{gathered} \frac{\left(10^4\right)^2\cdot\:10^(19)}{\sqrt{10^(-16)}}=(10^8\cdot10^(19))/(10^(-8))=10^8\cdot10^8\cdot10^(19)=10^(8+8+19)=10^(35) \\ \Rightarrow\log 10^(35)=35 \end{gathered}`

Therefore, the answer is 35