Wavelength with P/Q exponent equation-solve for P/Q

[afg_91320]

Homework Statement

Speed of an ocean wave depends on the wavelength \lambda in meters and
gravitational field. (see equation below). Find values of P and Q. K is a constant and has no dimensions

Homework Equations

V = K\lambda^Pg^Q

The Attempt at a Solution

V=velocity, which is m/s
and i can disregard K because it is a constant which has no dimensions.
g = m/s²
\lambda = m
plugging in the numbers; i get:

m/s = m^P(m/s²)^Q

here is where i get lost. i don't know how to bring the exponents down so i can solve for it

 

[Mark44]

You have V = K L^Pg^Q
(I used L in place of lambda.)
So L^P = V/[K g^Q]

To solve for P, take the log of both sides, then divide both sides by log L.

To solve for the other exponent Q, first solve for g^Q in a way similar to how I solved for L^P, then take the log of both sides, and divide both sides by log g.

 

[afg_91320]

are you sure? i was workin on this with my prof and he told me not to take the log; that's what i thought of doing initially
and i have no numerical values for the equations; its all dimension analysis

 

[Mark44]

OK, what's the exact statement of the problem? As you have it in post 1, it appears that you need to solve for P and Q.

 

[afg_91320]

The speed of ocean waves depend on their wavelength \Lambda (measured in meters) and the gravitational field strength g (measured in m/s^2) in this way:

v = \Lambda^Pg^Q

where K is a dimensionless constant. Find the values of the exponents P and Q