The functions 𝑔 and ℎ are given by 𝑔⁡(𝑥)=log4⁡(2⁢𝑥) ℎ⁡(𝑥)=(𝑒𝑥)5𝑒(1/4).(i) Solve 𝑔⁡(𝑥)=3 for values of 𝑥 in the domain of 𝑔.

Question

The functions 𝑔 and ℎ are given by

𝑔⁡(𝑥)=log4⁡(2⁢𝑥)
ℎ⁡(𝑥)=(𝑒𝑥)5𝑒(1/4).
(i) Solve 𝑔⁡(𝑥)=3 for values of 𝑥 in the domain of 𝑔.

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Solution

To solve the equation g(x) = 3 for values of x in the domain of g, we first need to understand what the function g(x) is.

The function g(x) is given by g(x) = log4(2x).

The logarithm equation can be rewritten in exponential form to solve for x.

So, if g(x) = 3, we have:

log4(2x) = 3

This can be rewritten in exponential form as:

4^3 = 2x

Solving for x gives:

x = 4^3 / 2 = 32

So, the solution to the equation g(x) = 3 for values of x in the domain of g is x = 32.

This problem has been solved

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