GCE O/L Mathematics (Sri Lanka) · Mathematics

Indices, Logarithms and Surds

43 practice questions, each with the answer and an explanation.

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All 43 questions

Find the value of $lo g_{3} 27$ .
Expand and simplify $(5 + 7) (5 - 7)$ .
Find $lo g_{3} 27 - lo g_{3} 9$ .
Simplify $\frac{3 ^{3} \times 3 ^{4}}{3 ^{2}}$ and give the answer as a power of $3$ .
Find the value of $lo g_{10} 2 + lo g_{10} 5$ .
Expand and simplify $(3 + 2) (3 - 2)$ .
Simplify $\frac{5 ^{3} \times 5 ^{5}}{5 ^{1}}$ and give the answer as a power of $5$ .
Simplify $180$ in the form $a b$ .
Find the value of $3^{- 2}$ .
Find the value of $lo g_{10} 2 + lo g_{10} 50$ .
Simplify $\frac{2 ^{6} \times 2 ^{4}}{2 ^{2}}$ and give the answer as a power of $2$ .
Find the value of $lo g_{10} 5 + lo g_{10} 20$ .
Simplify $63$ in the form $a b$ .
Evaluate $3 2^{\frac{3}{5}}$ .
Find $lo g_{2} 64 - lo g_{2} 2$ .
Simplify $75$ in the form $a b$ .
Simplify $\frac{2 ^{3} \times 2 ^{4}}{2 ^{1}}$ and give the answer as a power of $2$ .
Simplify $18$ in the form $a b$ .
Find $lo g_{3} 243 - lo g_{3} 81$ .
Expand and simplify $(5 + 5) (5 - 5)$ .
Find the value of $lo g_{10} 25 + lo g_{10} 4$ .
Evaluate $75 \times 3$ .
Find the value of $1 0^{- 3}$ .
Simplify $108$ in the form $a b$ .
Find $lo g_{2} 32 - lo g_{2} 16$ .
Simplify $175$ in the form $a b$ .
Simplify $\frac{3 ^{5} \times 3 ^{3}}{3 ^{3}}$ and give the answer as a power of $3$ .
Evaluate $100 0^{\frac{2}{3}}$ .
Find $lo g_{3} 729 - lo g_{3} 3$ .
Simplify $\frac{2 ^{6} \times 2 ^{3}}{2 ^{3}}$ and give the answer as a power of $2$ .
Find the value of $lo g_{10} 4 + lo g_{10} 25$ .
Find the value of $3^{- 1}$ .
Find $x$ if $2^{x + 1} = 128$ .
Find the value of $lo g_{2} 8$ .
Find the value of $4^{- 3}$ .
Find the value of $lo g_{5} 125$ .
Simplify $72$ in the form $a b$ .
Find $lo g_{2} 16 - lo g_{2} 2$ .
Find $lo g_{2} 64 - lo g_{2} 8$ .
Evaluate $2 7^{\frac{2}{3}}$ .
Find $lo g_{3} 81 - lo g_{3} 3$ .
Expand and simplify $(9 + 5) (9 - 5)$ .
Find the value of $1 0^{- 1}$ .

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