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BECE Mathematics 2022 Paper

Question : 28

Total: 40

x

3^x=81 ?

Solution:

Convert the 81 to

3^y

, where

y

is the power that will produce 81

81=3 \times 3 \times 3 \times 3

From the law of indices,

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

81=3 \times 3 \times 3 \times 3=3^{1+1+1+1}=3^4

Now replace 81 by

3^4

in the equation

\;3^x=81

\;3^x=3^4

Since the bases are the same, the powers are also the same Hence

x=4

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