2^2x . 5^(x-3)=10^(x+2)
How many people will be needed to count 47.8 million households if they work an average of 3.7 hours per day, 5 days a week for 10 weeks and they count 1.18 households per hour?
Each person can count how many households in that period of time?
3.7 hrs/day x (5 days/wk) x (10 wk) x 1.18 households/hr) = ?? households counted/counter.
Then 47.8 million households x (1 counter/??households) = xx
Check my work. Check for typos.
To solve the equation 2^(2x) * 5^(x-3) = 10^(x+2), we need to simplify the expression on each side and bring it to a common base.
Step 1: Rewrite 10 as the product of 2 and 5: 10 = 2 * 5. So, we have:
2^(2x) * 5^(x-3) = (2 * 5)^(x+2)
Step 2: Simplify the right side of the equation using the exponent properties. When raising a product to an exponent, we can distribute the exponent to each term. So, we can rewrite the right side as:
2^(2x) * 5^(x-3) = 2^(x+2) * 5^(x+2)
Now both sides have the same bases (2 and 5). So, we can equate the exponents:
2x = x + 2
x = 2
Thus, the solution to the equation is x = 2.