# Thread: Indices & Logarithm: If u = log_4(x), show that log_x(4) = 1/u. Hence,...

1. ## Indices & Logarithm: If u = log_4(x), show that log_x(4) = 1/u. Hence,...

I can stuck on this question and unable to do it.

If u = log4(x), show that logx(4) = 1/u. Hence, find values of x for which:

. . . . .2 log4(x) + 3logx(4) = 7

2. What have you tried or thought about, so far?

The first part of this exercise can be started with the Change of Base Formula or by switching to exponential form, and then thinking about the definitions of rational exponents. Maybe they're trying to demonstrate the relationship:

base^exponent = power

power^(1/exponent) = base

For example:

3^5 = 243

243^(1/5) = 3

For the second part, start by thinking about the first few powers of four, and for each power write out the values of the log expressions from the first part. Then check: Do any of these values satisfy the equation?

3. Originally Posted by Jx Chen
I can stuck on this question and unable to do it.

If u = log4(x), show that logx(4) = 1/u. Hence, find values of x for which:

. . . . .2 log4(x) + 3logx(4) = 7

What are your thought? What have you tried? Where are you stuck?

For instance, you started by converting the given log equation into its corresponding exponential equation:

. . . . .u = log_4(x)

. . . . .4^u = x

Then you took the base-x log of either side, applied the relevant log rule, divided through by the u, and... then what?