The functions 𝑔 and ℎ are given by 𝑔(𝑥)=log4(2𝑥) 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(2𝑥) ℎ(𝑥)=(𝑒𝑥)5𝑒(1/4).(i) Solve 𝑔(𝑥)=3 for values of 𝑥 in the domain of 𝑔.
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.
Similar Questions
The functions 𝑔 and ℎ are given by 𝑔(𝑥)=log5(4𝑥-2) ℎ(𝑥)=sin-1(8𝑥).(i) Solve 𝑔(𝑥)=3 for values of 𝑥 in the domain of 𝑔.(ii) Solve ℎ(𝑥)=𝜋4 for values of 𝑥 in the domain of ℎ.
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