Question Bank

Achieved

Find the value of $x$ if $2^{x-3} = 32$.

Achieved

Find the co-ordinates of the y-intercept for the exponential graph $y = 4(3^{2x-1}) + 7$.

Achieved

Find the coordinates of the y-intercept for the exponential graph $y = (\frac{1}{2})^{x-3} - 5$.

Achieved

The diagram below shows the graphs of $y = (1.2)^x$ and $y = \frac{1}{2}x + 1$.

Diagram

Use the graph to estimate the solutions to the equation $1.2^x = \frac{1}{2}x + 1$.

Achieved

Simplify the following expression:

$ \frac{\displaystyle 5^{4m-2}}{\displaystyle 5^{m+4}} $

Achieved

Simplify the following expression:

$ 3^{p+1} \times 9^{2p-5} $

Achieved

Simplify the following expression:

$ 2^{a+2} \times 4^{2a-1} \times 2^{-3a} $

Merit

Solve the equation $9^{2x-1} = 27^{x+4}$.

Merit

Find the value of $x$ by solving the equation $8^{x+3} = 16^{x-1}$.

Merit

Solve for $x$ in the equation $25^{2x} = (\frac{1}{125})^{x-5}$.

Excellence

Make $y$ the subject of the formula $\frac{8^{x+2}}{4^x} = 2^{5y-1}$.

Excellence

Make $y$ the subject of the formula $25^{x-1} \times 5^{3x+1} = 125^{y+2}$.

Excellence

Find the values of $x$ by solving the equation $9^{x^2} \times 3^{5x} = \frac{1}{9}$.

Excellence

Given the equation $6^{2x} + 6^{2x} + 6^{2x} + 6^{2x} + 6^{2x} + 6^{2x} = 6^y$, find an expression for $y$ in terms of $x$.