Question

12,067 Learners found this answer helpful

solve. write your answer as an integer or a fraction in simplest form.
$1 = 7^{3x + 4}$
$x = \square$

Explanation:

Step1: Rewrite 1 as 7 to a power

Any non-zero number to the 0 power is 1, so $1 = 7^0$.
The equation becomes:
$$7^0 = 7^{3x+4}$$

Step2: Set exponents equal

If $a^m = a^n$ (where $a>0, a
eq1$), then $m=n$.
$$0 = 3x + 4$$

Step3: Solve for x

Subtract 4 from both sides, then divide by 3.
$$3x = -4$$
$$x = \frac{-4}{3}$$

Answer:

$\boldsymbol{-\frac{4}{3}}$