Question

$\frac{5 \times {3}^{x} - 9 \times {3}^{x - 2} }{ {3}^{x} - {3}^{x - 1} }$
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Answer 1

ANSWER:

• THE VALUE OF THIS EXPRESSION IS 6.

GIVEN:

$\frac{5 \times 3 {}^{x} - 9 \times 3 {}^{x - 2} }{3 {}^{x} - 3 {}^{x - 1} }$

TO FIND:

The value of the above expression.

SOLUTION:

$= \frac{5 \times 3 {}^{x} - 9 \times 3 {}^{x - 2} }{3 {}^{x} - 3 {}^{x - 1} } \\ = \frac{5 \times 3 {}^{x} - 3 { }^{2} \times 3 {}^{x - 2} }{3 {}^{x} - 3 {}^{x } \times 3 {}^{ - 1} } \\ = \frac{5 \times 3 {}^{x} - 3 {}^{x - 2 + 2} }{3 {}^{x} - \frac{3 {}^{x} }{3} } \\ = \frac{5 \times 3 {}^{ x} - 3 {}^{x} }{3 {}^{x}(1 - \frac{1}{3} ) } \\ = \frac{3 {}^{x} (5 - 1)}{3 {}^{x}( \frac{2}{3} )} \\ \implies \: 3 {}^{x} \: will \: be \: cancel \: out \\ = 4 \times \frac{3}{2} \\ = 6$

THE VALUE OF THIS EXPRESSION IS 6.

NOTE:

some important formulas:

$\implies \: a {}^{m} \times a {}^{n} = a {}^{m + n} \\ \implies \: a {}^{m} \div a {}^{n} = a {}^{m - n} \:$