Question

If (3³)² = 9ˣ then 5ˣ = ?

Answer 1

Answer:

(5^2)^2=5^x is the answer

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ {( {3}^{3} )}^{2} = {9}^{x} }$

TO DETERMINE

$\displaystyle \sf{ {5}^{x} }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that :

‌$\sf{1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} }$

‌$\displaystyle \sf{2. \: \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

‌$\displaystyle \sf{3. \: \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

‌$\displaystyle \sf{4. \: \: {a}^{0} = 1}$

EVALUATION

$\displaystyle \sf{ {( {3}^{3} )}^{2} = {9}^{x} }$

$\displaystyle \sf{ \implies ( {3}^{3 \times 2} ) = {( {3}^{2} )}^{x} }$

$\displaystyle \sf{ \implies ( {3}^{6} ) = {3}^{2x} }$

$\displaystyle \sf{ \implies {3}^{2x} = {3}^{6} }$

$\displaystyle \sf{ \implies 2x = 6}$

$\displaystyle \sf{ \implies x = 3}$

Now

$\displaystyle \sf{ {5}^{x} }$

$\displaystyle \sf{ = {5}^{3} }$

$\displaystyle \sf{ = 125 }$

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