BECE Mathematics 2020 Paper

Question : 29

Total: 40

Solve:

4^x=32

Solution:

Make sure both sides of the equation are in the same base

4 and 32 can both be expressed in base 2

Applying the law of indices,

a^{b} \times a^{c}=a^{b+c}

, thus you add the powers if they are multiplying and the bases are the same

\;4=2 \times 2=2^1 \times 2^1=2^{1+1}=2^2

\;32=2 \times 2 \times 2 \times 2 \times 2=2^{1+1+1+1+1}=2^5

\;4^x=32

\; \Rightarrow (2^2) ^x=2^5

Applying the law of indices,

(a^n) ^m=a^{n \times m}

\Rightarrow 2^{2 x}=2^5

Since the bases are the same, the powers must also be the same

\Rightarrow 2 x=5

Divide both sides by 2

\Rightarrow x=\frac{5}{2}=\frac{21}{2}

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