What power of 10 would make the following equation true?

Question

7.34 x 10 x
 = 0.000734

(1 point)
Responses

-4
-4

4
4

6
6

-5
-5

Answer 1

To solve for the power of 10 in the equation $7.34\times {10}^x=0.000734$, we first need to express $0.000734$ in terms of a power of 10.

We can rewrite $0.000734$ as follows:

$$0.000734=7.34\times {10}^{-4}$$

Now we can substitute this back into the equation:

$$7.34\times {10}^x=7.34\times {10}^{-4}$$

Since both sides have $7.34$, we can divide both sides by $7.34$:

$${10}^x={10}^{-4}$$

This implies that:

$$x=-4$$

Thus, the value of $x$ that makes the equation true is:

$$\boxed{{\displaystyle -4}}$$