Surds, Indices and Logarithms
GCE Further Mathematics

1. (a) Without using tables or calculator, simplify: (√75 - √48) / √3, leaving your answer in the simplest form. [4 marks] (b) Given that log₂(x + 3) + log₂(x - 1) = 5, find the value(s) of x. [6 mar…

2. (a) Rationalise the denominator and simplify: (4 + √5) / (√5 - 1), leaving your answer in the form p + q√5, where p and q are rational numbers. [5 marks] (b) (i) Show that log_a(x) = log_b(x) / lo…

Evaluate $\frac{3^{n+1} - 3^n}{3^{n-1}}$

Rationalize the denominator of $\frac{5}{3 - \sqrt{2}}$ and simplify.

Given that log 2 = 0.3010 and log 3 = 0.4771, find log 72.

Simplify √75 + √48 − √27

If $\log_x 64 = 3$, find x.

Simplify $\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$

Find the value of $x$ if $\log_3(x^2 - 2x) = 1$.

Solve for x: $2^{2x} - 5(2^x) + 4 = 0$

If log₂ 8 + log₂ 4 = log₂ x, find x.