1110
Starting with
The left-hand side is just y; using the laws of exponents on the right-hand side we get
Since 10^(ab) = (10^a)^b the factor 10^(5 log(x)) = (10^(log(x))^5) so
So y is a power function of form y = A x^p with A = 10^7 and p = 5.
Starting with
The left-hand side is just y; using the laws of exponents on the right-hand side we get
Since 10^(ab) = (10^a)^b the factor 10^(5 x) = (10^5)^x so
This function is an exponential function of form y = A b^x with A = 10^7 and b = 100,000.
Generalizing:
If
then when we solve for y we get a power function.
If
then when we solve for y we get an exponential function.
If we have a table of y vs. x data, then if a graph of log(y) vs. log(x) gives us a straight line, we can find the slope m and the y-intercept b and get the equation log(y) = m log(x) + b.
Of a graph of log(y) vs. x is linear, then the slope and y intercept will give us the form log(y) = m x + b.