Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 15, 2023

Solve the equation $7^{x^{2}-6x}=1$ .

STEP 1

Assumptions1. The equation is $7^{x^{}-6 x}=1$ . We are looking for all possible real values of $x$ that satisfy the equation

STEP 2

We know that any number raised to the power of0 is1. Therefore, we can set the exponent of7 equal to0.
$x^{2}-6 x=0$

STEP 3

This is a quadratic equation. We can solve it by factoring.
$x(x-6)=0$

STEP 4

Setting each factor equal to zero gives the solutions to the equation.
$x=0$ and $x-6=0$

STEP 5

olving the second equation gives the second solution.
$x=$ So, the solutions to the equation $7^{x^{2}- x}=1$ are $x=0$ and $x=$ .

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