Question

Chapter 5:Indices and Logarithms
@ganeshie8

Answer 1

\[Given~\log _{3}x=7~and~\log _{3}y=3,\]find the values of:\[\log _{3}\frac{ y^2 }{ \sqrt{3x} }\]

Answer 2

My answer is 2 but the answer in the book say it's 9

Answer 3

im also getting 2

Answer 4

\[=\log _{3}y+\log _{3}y-(\log _{3}\sqrt{3}+\log _{3}\sqrt{x})\]

Answer 5

\[=3+3-(\frac{ 1 }{ 2 }+\frac{ 7 }{ 2 })\]

Answer 6

Looks neat !

Answer 7

\[=6-4\]\[=2\]

Answer 8

hmmm

Answer 9

\[3^{\log_{3}x}=3^7\]\[x=3^7\]\[3^{\log_{3}y}=3^3\]\[y=3^3\]\[\log_{3}\frac{y^2}{\sqrt{3x}}=\log_{3}y^2-\log_{3}(3x)^{1/2}=2\log_{3}y-\frac{1}{2}(\log_{3}3+\log_{3}x)=(2 \times 3)-\frac{1}{2}(1+7)\]
\[6-(\frac{1}{2} \times8)=6-4=2\]