Solve log 2x + log 12 = 3. Round to the nearest hundredth if necessary.

Question

(1 point)
Responses

6,000
6,000

24,000
24,000

166.67
166.67

41.67

Answer 1

To solve the equation log 2x + log 12 = 3, we can combine the logarithms using the product rule:

log (2x)(12) = 3
log (24x) = 3

Now we can rewrite this in exponential form:

10^3 = 24x
1000 = 24x
x = 1000/24
x = 41.67

Therefore, the solution to log 2x + log 12 = 3 is x = 41.67. Rounded to the nearest hundredth, x ≈ 41.67.

So the answer is 41.67.