How do you solve #1/ sqrt 8 = 4^(m – 2)#?

1 Answer
Daniel L.
Feb 14, 2016

The answer is #m=1 1/4#

Explanation:

When solving exponential equations (or inequalities) first you have to find a suitable common base. In this case it would be #2# because #8=2^3# and #4=2^2#.

Now you have to write the equation using calculated base:

#1/sqrt(2^3)=2^(2*(m-2))#

Now you can use the property of powers which says that #root(n)(a)=a^(1/n)#

#1/2^(3/2)=2^(2m-4)#

Next property to use is: #1/(a^x)=a^(-x)#

#2^(-3/2)=2^(2m-4)#

Now since we have the equality of 2 powers with equal base we can write it as the equality of exponents:

#-3/2=2m-4#

#2m=4-3/2#

#2m=2 1/2#

#2m=5/2#

#m=5/4=1 1/4#

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