Practise online Get the app

Paper 2 · November 2023 · Logarithms and Exponentials

Simplify $\dfrac{3^{2x-3}\cdot81^{x+\frac12}}{27^x}$ , giving the answer as a single power of 3.

Model answer

3^(3x-1)

Also accepted: 3^{3x-1}, 3^(3x - 1)

Explanation

Write every base as a power of 3:

81^{x+\frac12}=3^{4x+2}

and

27^x=3^{3x}

. The numerator is

3^{2x-3}\cdot3^{4x+2}=3^{6x-1}

, so the quotient is

3^{6x-1-3x}=3^{3x-1}

.

Derived from ZIMSEC Pure Mathematics Paper 2, November 2023, Q1

View this paper's sittings and topics→

More questions from this paper

The extension $y$ of an elastic string varies directly as the magnitude of the force $F$ extending it. Given $y=0.45$ m when $F=6$ N, express $F$ as a function of $y$ .
Solve the inequality $|x^2-2|<-x$ .
In solving $|x^2-2|<-x$ by cases, why is only $x=-2$ (not $x=1$ ) accepted from the case $x^2-2\ge0$ , and only $x=-1$ (not $x=2$ ) accepted from the case $x^2-2<0$ ?
The graph $y=f(x)$ has $y$ -intercept $(0,16)$ . State the $y$ -intercept of $y=f(x)-6$ .
The graph $y=f(x)$ has $x$ -intercepts $(-2,0)$ , $(2,0)$ and $(4,0)$ . State the $x$ -intercepts of $y=f(x+1)$ .

Get the full paper, not just one question

Danho has every sitting for this paper, with your progress tracked question by question, offline.

Get it on Google Play Download on the App Store