IB Maths AA SL AA 1.2 practice question

Paper 1, no calculatorMedium6 marks

Let $p=\log_2 3$ and $q=\log_2 5$ Consider the equation

4^{x+\frac12}=\frac{5\times81^{\frac34}}{3},\qquad x\in\mathbb R.

(a)

Find the value of $81^{\frac34}$

[1]

(b)

Show that

\log_2\left(\frac{5\times81^{\frac34}}{3}\right)=2p+q.

[2]

(c)

Hence solve the equation, giving your answer in terms of $p$ and $q$

[3]