Question

The variables x and y are connected by an equation of the form y= ax^b. when a graph of lg y against lg x is plotted, a gradient of 1.5 and a lgy intercept of 1.2 are obtained. What are values a and b?

Answer 1

The given equation `y= ax^b`

Taking `log_10` we get

`log_10y=log_10( ax^b)`

`\>log_10y=log_10 a+blog_10x`

when a graph of `log_10 y` against `log_10 x` is plotted, a gradient `1.5` and intercept 1,2 are obtained. So `b=1.5`

and `" "log_10 a=1.2=>a=10^1.2`