How do you solve $\sqrt { 125} = 5^ { x }$ ?

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Answer 1 · 2018-06-30T20:54:43

$x = 3/2$

$sqrt(125) = 125^(1/2)$

$125 = 5^3$

$=> 125^(1/2) = (5^3)^(1/2)$

$=> 5^x = (5^3 ) ^(1/2)$

$=> 5^x = 5^(3/2)$

Considering the exponents:

$x = 3/2$

Answer 2 · 2018-06-30T21:08:23

$x=3/2$

We can rewrite $sqrt125$ as $125^(1/2)$ . This now gives us

$125^(1/2)=5^x$

Let's make our bases the same. $125=5^3$ , so we can rewrite the equation as

$5^(3(1/2))=5^x$

Since our bases are the same, the exponents are equal.

$5^(3/2)=5^x$

$=>3/2=x$

$x=3/2$

Hope this helps!

How do you solve \sqrt { 125} = 5^ { x }\sqrt { 125} = 5^ { x }?