How do you solve #10^(4x -1) = 1000# and find any extraneous solutions?

Question

2580 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-05T18:57:55

The only solution is #x=1#.

Rewrite #1000# as #10^3#:

#10^(4x-1)=1000#

#10^(4x-1)=10^3#

Now, since the bases are the same, the exponents must be equal to each other:

#10^color(red)(4x-1)=10^color(red)3#

#4x-1=3#

#4x=4#

#x=1#

This is the only solution. We can verify it by plugging it back into the original equation:

#10^(4(1)-1)=1000#

#10^(4-1)=1000#

#10^3=1000#

#1000=1000#

Hope this helped!