An algebra problem by Naveed Malik

Algebra Level 1

$\large \begin{aligned} 4^{x}-4^{x-1}&=12 \\ x^{x}&= \ ? \end{aligned}$

9 4 2 16 8

2 solutions

A Former Brilliant Member
Jun 20, 2016

$\Rightarrow 4^x-4^{x-1}=12$

$4^x\left(1-\dfrac{1}{4}\right)=12$

$4x\left(\dfrac{3}{4}\right)=12$

$4^x=12×\dfrac{4}{3}$

$4^x=4^2$

$x=2$

$\huge \therefore x^x=2^2=\color{#20A900}{\boxed{4}}$

Naveed Malik
Jun 20, 2016

we put X=2 $4^{2}-4^{2-1}=12$ $2^{2}=4ans$

How do we know that we should put $x=2$ ???

Hung Woei Neoh - 4 years, 11 months ago

because of equality, equation is equal to 12 we have to gauss we should put x=2 otherwise we can use abhay kumar method

Naveed Malik - 4 years, 11 months ago

What if there is no option given in this question?Then, what you will do?

A Former Brilliant Member - 4 years, 11 months ago

@A Former Brilliant Member – i am talking about this equation which is given and equal to 12 which tells us we have to put X=2 for l.h.s=r.s.h $4^{x}-4^{x-1}=12$

Naveed Malik - 4 years, 11 months ago

@Naveed Malik – Exactly my point. How did you deduce, without any steps or working, that $x=2$ ? Why must we guess that $x=2$ ?

Hung Woei Neoh - 4 years, 11 months ago

@Hung Woei Neoh – if you put 1,3 or any other real no than equation does not satisfies. it is your iq that tells you what we have to put this is a short mcq you have only 25-35s to solve it. $4^{1}-4^{1-1}\neq 12$ $4^{2}-4^{2-1}=12$ $4^{3}-4^{3-1}\neq 12$ $4^{4}-4^{4-1}\neq 12$

Naveed Malik - 4 years, 11 months ago

@Naveed Malik – So basically you are saying that we should be able to see the answer just by looking at the equation?

Hung Woei Neoh - 4 years, 11 months ago

@Hung Woei Neoh – yes exactly you have to judge or calculate ans in your mind rapidly.

Naveed Malik - 4 years, 11 months ago

@Naveed Malik – When answering a question, yes, this judgement and intuition is needed to solve it quickly. I agree with this.

However, this is a solution you're writing, which is meant to help others who can't see the answer directly learn the steps to solve this equation. Solutions are supposed to have adequate proof or working to guide others. If not, there's no reason to write a solution at all.

Hung Woei Neoh - 4 years, 11 months ago

An algebra problem by Naveed Malik

2 solutions

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