Here are the two methods of solution:
Write the equation: | 1000(1.10)4x = 2000 | |
Make sure it has the form A = bc : | No! So make it have that form (divide both sides by 1000). | |
Divide both sides by 1000: | 1.104x = 2000/1000 = 2 | |
Rewrite in logarithmic form: | 4x = log1.10 2 | |
Solve for x: | x = (log1.10 2)/4 ≈ 1.818 |
Solution Method 2 (Taking the Log of Both Sides):
Write the equation: | 1000(1.10)4x = 2000 | |||||
Take the natrual log of both sides: (You don't have to take log to the base 1.10) | ln[1000(1.10)4x] = ln 2000 | |||||
Use rule(1) Note this step!: | ln 1000 + ln(1.104x) = ln 2000 | |||||
Reorganize: | ln(1.104x) = ln 2000 - ln 1000 | |||||
Simplify right-hand side using rule (2): | ln(1.104x) = ln(2000/1000) = ln 2 | |||||
Use rule(3): | 4x ln 1.10 = ln 2 | |||||
Solve for x: |
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