If $$ 6^{4 x-1}=6^{7} $$, then $$ \square=7 $$

Question

UpStudy AI · Accepted Answer

To solve the equation $$ 6^{4x-1} = 6^{7} $$, we can use the property of exponents that states if the bases are the same, then the exponents must be equal.

1. Set the exponents equal to each other:
   $$
   4x - 1 = 7
   $$

2. Solve for $$ x $$:
   - First, add 1 to both sides:
   $$
   4x = 7 + 1
   $$
   $$
   4x = 8
   $$

- Next, divide both sides by 4:
   $$
   x = \frac{8}{4}
   $$
   $$
   x = 2
   $$

Thus, the value of $$ x $$ is $$ 2 $$.

Now, according to your statement, $$ \square = 7 $$. However, the solution we found is $$ x = 2 $$.

If you meant to find the value of $$ 4x - 1 $$ instead, we can substitute $$ x = 2 $$ back into the expression:

$$
4(2) - 1 = 8 - 1 = 7
$$

So, indeed, $$ \square = 7 $$ is correct if $$ \square $$ represents $$ 4x - 1 $$.

Final answer:
$$
\boxed{7}
$$
$$ x = 2 $$

If \( 6^{4 x-1}=6^{7} \), then \( \square=7 \)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Algebra Questions