Can someone explain the equation #16^(2x-5) = 1# step by step please?

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Answer 1 · 2018-04-27T14:19:04

#x=5/2=2.5#

Given: #16^(2x-5)=1#.

Know that #a^0=1,a!=0,ainRR#.

So, we can write #1# as #1=16^0#.

Therefore, the equation becomes:

#16^(2x-5)=16^0#.

Now, it is to spot that #2x-5# must equal to #0#.

We get:

#2x-5=0#

Add #5# to both sides.

#2x-color(red)cancelcolor(black)5+color(red)cancelcolor(black)5=0+5#

#2x=5#

Divide by #2# on both sides.

#(color(red)cancelcolor(black)2x)/(color(red)cancelcolor(black)2)=5/2#

#x=5/2=2.5#