Final answer:
To find the value of k that makes the equation true, divide both sides of the equation by 3.42891 to isolate the exponential term. Rewrite 0.0001 as 1 × 10^-4. Equate the exponents to find that the value of k is -4.
Step-by-step explanation:
To find the value of k that makes the equation 0.000342891 = 3.42891 х 10* TRUE, we need to solve for k. First, we can rewrite the equation as 0.000342891 = 3.42891 × 10^k. Since the base of the exponent is the same, we can equate the two numbers: 0.000342891 = 3.42891 × 10^k.
Next, we can divide both sides of the equation by 3.42891 to isolate the exponential term: 0.000342891 / 3.42891 = (3.42891 × 10^k) / 3.42891. Simplifying this gives us: 0.0001 = 10^k.
Finally, we can rewrite 0.0001 as 1 × 10^-4. So, we have 10^-4 = 10^k. Since the bases are the same, we can equate the exponents: -4 = k. Therefore, the value of k that makes the equation true is -4.