Logarithmic graphs Quiz

1. A graph of $\lg y$ against $\lg x$ is a straight line with gradient $3$ and intercept $1$. Which relationship does this give?

• A. $y=3x^{10}$
• B. $y=10x^3$
• C. $y=3\times10^x$
• D. $y=10\times3^x$

2. A graph of $\lg y$ against $x$ has gradient $0.5$ and intercept $1.2$. Which gives $k$ and $b$ in $y=kb^x$?

• A. $k=1.2$, $b=0.5$
• B. $k=3.16$, $b=15.8$
• C. $k=15.8$, $b=3.16$
• D. $k=10^{0.5}$, $b=10^{1.2}$

3. Data satisfy $y=ax^n$. Which two quantities should be plotted to obtain a straight line?

• A. $y$ against $x$
• B. $\lg y$ against $x$
• C. $y$ against $\lg x$
• D. $\lg y$ against $\lg x$

4. A straight line of $\lg y$ against $x$ passes through $(2,1.7)$ and $(6,3.3)$. Find $b$ in $y=kb^x$ to 3 s.f.

• A. $2.51$
• B. $0.4$
• C. $1.6$
• D. $25.1$

5. A line of $\lg y$ against $\lg x$ passes through $(1,2)$ and $(3,4)$. Find $y$ when $x=10$.

• A. $10$
• B. $1000$
• C. $100$
• D. $10\,000$