Laws of exponents

Algebra Level 1

If ( m + 2 ) ( m 2 − 4 ) = ( m + 2 ) x ( m − 2 ) (m+2)(m^2-4)=(m+2)^x(m-2) for all values of m m , what is the value of x x ?

1 3 4 2

A Former Brilliant Member by A Former Brilliant Member

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Mohammad Khaza
Oct 2, 2017

( m + 2 ) ( m 2 − 4 ) (m+2)(m^2-4) = ( m + 2 ) x ( m − 2 ) (m+2)^x(m-2)

or, ( m + 2 ) ( m 2 − 2 2 ) (m+2)(m^2-2^2) = ( m + 2 ) x ( m − 2 ) (m+2)^x(m-2)

or, ( m + 2 ) ( m + 2 ) ( m − 2 ) (m+2)(m+2)(m-2) = ( m + 2 ) x ( m − 2 ) (m+2)^x(m-2) .................[dividing both sides by (m-2)]

or, ( m + 2 ) 2 = ( m + 2 ) x (m+2)^2=(m+2)^x

or, x = 2 x=\boxed2

1 Helpful 0 Interesting 0 Brilliant 0 Confused

( m + 2 ) ( m 2 − 4 ) = ( m + 2 ) x ( m − 2 ) (m+2)(m^2-4)=(m+2)^x(m-2)

Factor the left side.

( m + 2 ) ( m + 2 ) ( m − 2 ) = ( m + 2 ) x ( m − 2 ) (m+2)(m+2)(m-2)=(m+2)^x(m-2)

( m + 2 ) 2 = ( m + 2 ) x (m+2)^2=(m+2)^x

2 = x \boxed{2=x}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...