Question

Solve 5x=125 using the one-to-one property of exponents.

A) X=In(125)
B) x = 1
C) x = 3
OD) x = 5

Answer 1

Since 125 is 25 times 5, I may rewrite it as 125 is 5 times 5 times 5. Add the exponents one plus one plus one using the same base. Simply put, this is five to the third power. because their bases are each five. Technically, since the university exponent is log, u could take the log, base five, of both sides, making X equal to 3.

Answer 2

C) x = 3

Explanation:

Given equation:

`5^x=125`

Rewrite 125 with base 5: 125 = 5³

`\implies 5^x=5^3`

`\textsf{Apply the one-to-one property of exponents}: \quad a^(f(x))=a^(g(x)) \implies f(x)=g(x)`

`\implies x=3`