Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Dec 04, 2023

Solve the exponential equation $7^{x}=1$ for the value of $x$ .

STEP 1

Assumptions
1. We are looking for the value of x such that $7^{x}=1$ .

STEP 2

We know that any non-zero number raised to the power of 0 equals 1. This is a basic rule of exponents.
$a^{0}=1$

STEP 3

In our case, the base is 7. So, we can equate the exponent of 7 to 0 to get 1.
$7^{x}=1$

STEP 4

Setting x to 0, we get:
$7^{0}=1$

STEP 5

So, the value of x that satisfies the equation $7^{x}=1$ is 0.
The solution is x = 0.

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