2. Solve 10^6x = 93. Round to the nearest ten-thousandth. (1 point)11.81091.098613.38010.32813. Use a graphing calculator. Solve 5.5^3x = 805 by graphing. Round to the nearest hundredth. (1 point)2.913.921.310.97,
Accepted Solution
A:
2. 0.3281 3. 1.31
2. 10^(6x) = 93 For this problem, using a calculator makes it quite simple. What you want is the power that you can raise 10 to that gives you 93. That value is the logarithm of 93 to base 10. So 10^(6x) = 93 log(10^(6x)) = log(93) 6x = 1.968482949 x = 0.328080491 x = 0.3281
3. This problem is both trickier and easier than the previous. All you need to do is plot the function on your calculator and look for the answer that's nearest which is 1.31, you could also get a more precise answer by calculating the logarithm to base 5.5 of 805. You won't find such a logarithm function on your calculator, but that isn't a major problem since you can easily convert a logarithm from any base to any other base by simply dividing by the logarithm of the desired base. So: 5.5^(3x) = 805 log(5.5^(3x)) = log(805) log(5.5^(3x))/log(5.5) = log(805)/log(5.5) log to base 5.5 of 5.5^(3x) = log(805)/log(5.5) 3x = 2.90579588/0.740362689 3x = 3.92482755 x = 1.30827585 x = 1.31