Question

What is the first step in the standard procedure for \[y=[u(x)]^{v(x)}\]?

Options

• Differentiate both sides before taking logarithm

• Take the natural logarithm \[\log_e\] or \[\ln\] on both sides: \[\log y=v(x)\cdot\log[u(x)]\]

• Multiply both sides by \[y\] before taking logarithm

• Replace \[v(x)\] by \[u(x)\] before taking logarithm

Answer 1

The first step is to take the natural logarithm on both sides. Thus \[\log([u(x)]^{v(x)})\] becomes \[v(x)\cdot\log[u(x)]\], bringing the exponent down.