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

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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!

How do you solve 10^(4x -1) = 100010^(4x -1) = 1000 and find any extraneous solutions?