Indices, Surds & Logarithms

m² × n³ × m⁶ =

• m⁸n³

• m⁶n³

• mn¹¹

• mnm¹¹

Find the value of x if 16^{2x − 1} = 64.

• 1.5

• 1.25

• −1.25

• $\frac{4}{5}$

Simplify  $\frac{3^n\times9^{n+1}}{3^{n-1}\times9^{n-1}}$ .

• 3

• 27

• 81

• 243

Simplify log₃ 9 + log₃ 27.

• −1

• 4

• 5

• 1

Evaluate 3 log₂ 4.

• 3

• 2

• 6

• 4

Write 5² = 25 in logarithmic equation.

• log₅ 2 = 25

• log₂₅ 5 = 2

• log₂ 25 = 5

• log₅ 25 = 2

Express $\log_2\left(\frac{1}{8}\right)=-3$  in index form.

•  $2^{-3}=\frac{1}{8}$  

•  $-3^2=\frac{1}{8}$  

•  $2^{\frac{1}{8}}=-3$  

•  $-3^{\frac{1}{8}}=2$  

Given log₅ (4x − 7) = log₅ (x + 5).

Find the value of x.

• 3

• 4

• 7

• 12

The diagram shows a right-angled triangle. Find the value of x.

• $3\sqrt{2}$

• $6\sqrt{8}$

• $8\sqrt{6}$

• $2\sqrt{3}$

The price of a house increases 5% from the original price at the beginning of every year. The original price of the house is RM90 000. After years, the price, in RM, is given by p = 90 000(1.05)^t. Calculate to the nearest RM, the price of the house after 6.5 years.

• RM123 587

• RM223 587

• RM132 876

• RM333 876