Question

, I'm having an issue with this logarithmic equation I will upload a photo

Answer 1

a)

`\begin{gathered} \log _a(1.8)= \\ =\log _a((9)/(5))= \\ =\log _a(9)-\log _a(5)= \\ =\log _a(3^2)-\log _a(5)= \\ =2\log _a(3^{})-\log _a(5)= \\ \approx2\cdot0.79-1.16\approx \\ \approx0.42 \end{gathered}`

b)

`\begin{gathered} \log _a(\sqrt[]{5})= \\ =\log _a(5^{(1)/(2)})= \\ =(1)/(2)\log _a(5)= \\ \approx(1)/(2)\cdot1.16\approx0.58 \end{gathered}`

c)

`\begin{gathered} \log _a(15)= \\ =\log _a(3\cdot5)= \\ =\log _a(3)+\log _a(5)= \\ \approx0.79+1.16\approx1.95 \end{gathered}`

d)

`\begin{gathered} \log _a(45)= \\ =\log _a(9\cdot5)= \\ =\log _a(9)+\log _a(5)= \\ =\log _a(3^2)+\log _a(5)= \\ =2\log _a(3^{})+\log _a(5)= \\ \approx2\cdot0.79+1.16\approx2.74 \end{gathered}`

e)

`\begin{gathered} \log _a(0.6)= \\ =\log _a((3)/(5))= \\ =\log _a(3)-\log _a(5)= \\ \approx0.79-1.16\approx-0.37 \end{gathered}`

f)

`\begin{gathered} \log _a(9)= \\ =\log _a(3^2)= \\ =2\log _a(3)= \\ \approx2\cdot0.79\approx1.58 \end{gathered}`