Question

n exact form 4, 4 marks b) $2^{x + 2}-2^{x}=18$ (answer as a fully reduced logarithm)

Explanation:

Step1: Factor out $2^x$

$2^x(2^2 - 1) = 18$

Step2: Simplify the bracket term

$2^x(4 - 1) = 18$
$2^x \times 3 = 18$

Step3: Isolate the exponential term

$2^x = \frac{18}{3}$
$2^x = 6$

Step4: Convert to logarithmic form

$x = \log_{2}6$

Step5: Simplify the logarithm

$x = \log_{2}(2 \times 3) = \log_{2}2 + \log_{2}3 = 1 + \log_{2}3$

Answer:

$x = 1 + \log_{2}3$ or $x = \log_{2}6$