If two physical quantites P and Q are related as P = kQⁿ, where K and n are unknown. we can reduce the expression to linear by

Question

If two physical quantites P and Q are related as P = kQⁿ, where K and n are unknown. we can reduce the expression to linear by

a.
taking exponential of both sides

b.
taking logarithm of both side

c.
diffrentiate both sides

d.
integrate both side

Answer 1

b. taking logarithm of both side

Answer 2

The correct answer is b. taking logarithm of both sides.

In order to reduce the expression to linear form, we can take the logarithm of both sides of the equation. This is because if we take the logarithm of P=kQ^n, we get log(P) = log(kQ^n).

Using logarithmic rules, we can simplify this expression further. The logarithm of a product is equal to the sum of the logarithms of the individual numbers, and the logarithm of a power is equal to that power times the logarithm of the number. Applying these rules, we get: log(P) = log(k) + log(Q^n).

Using another logarithmic rule, we can bring the power n down as a coefficient: log(P) = log(k) + n*log(Q).

Now, the equation is in linear form, where log(P) is the dependent variable and log(Q) is the independent variable. The coefficient n represents the slope of the linear function, and log(k) is the y-intercept.

By taking the logarithm of both sides, we have converted the equation into a linear form, allowing us to analyze the relationship between P and Q more easily.

Answer 3

To reduce the expression P = kQⁿ to a linear form, we need to remove the exponent (ⁿ) by taking logarithm of both sides. Therefore, the correct option is b. taking logarithm of both sides.

By taking the logarithm of both sides, we can use logarithmic rules to eliminate the exponent and make the equation linear. Taking the natural logarithm (ln) of both sides gives:

ln(P) = ln(kQⁿ)

Then, we can use the logarithmic property ln(a^b) = b ln(a) to simplify as:

ln(P) = ln(k) + n ln(Q)

Now, we have reduced the expression to a linear form with ln(P) on the left side and ln(Q) on the right side. This allows us to apply linear regression techniques to determine the values of k and n by plotting ln(Q) versus ln(P) and finding the slope and intercept of the resulting line.