Challenging equation that have exponential variable

Algebra Level 1

Solve for $x$ : $3^{x} + 3^{x + 2} - 3= 267$

The answer is 3.

3 solutions

A Former Brilliant Member
Oct 3, 2015

To find x .
In the eqution,
$3^{x}$ + $3^{x+2}$ -3=267
$3^{x}$ + $3^{x+2}$ =270
$3^{x}$ + $3^{x+2}$ = $3^{3}$ ×10
Now on comparing ,
$3^{x}$ = $3^{3}$
$x$ = $3$

Same solution here, thanks for posting it :)

Don Ramon De Jesus - 5 years, 8 months ago

Thanks! :)

A Former Brilliant Member - 5 years, 8 months ago

Instead of comparing we can just do this instead, $3^{x}(1+3^2) = 270 \Rightarrow 3^{x} \times 10 =270 \Rightarrow 3^x =27$ Now its quite obvious that $x=\boxed{3}$

Athiyaman Nallathambi - 5 years, 8 months ago

Mohit Gupta
Oct 3, 2015

Well sorry to say that but in what terms is this eqn. challenging??????????

Mohammad Khaza
Jul 7, 2017

3^x + 3^(x+2) - 3=267

or, 3^x(1 + 3^2) =270

or,3^x . 10 =270

or, 3^x = 27

or, 3^x = 3^3

or, x=3

Challenging equation that have exponential variable

The answer is 3.

3 solutions

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