Question

If 5* = 1, the value of x is.​

Answer 1

Answer:

5x=1

x=1/5

the value of x=1/5

Answer 2

Required Answer:-

Given:

• 5^x = 1

To find:

• The value of x.

Answer:

• The value of x is 0.

Solution:

$\sf {5}^{x} = 1$

$\sf \implies {5}^{x} = {5}^{0}$

Comparing base, we get,

$\sf \implies x = 0$

Hence, the value of x is 0

Note:- Any number(except 0) raised to the power zero is always 1.

Proof:-

Let the number be x where x ≠0

So,

$\sf {x}^{0}$

$\sf = {x}^{2 - 2}$

$\sf = {x}^{2} \times {x}^{ - 2}$

$\sf = {x}^{2} \times \frac{1}{ {x}^{2} }$

Now, cancel x² . We get,

$\sf = 1$Hence, any number(except 0) raised to the power 0 is always 1.