Here are the two methods of solution:
Write the equation: | 3(24x) = 192 | |
Make sure it has the form A = bc : | No! So make it have that form (divide both sides by 3). | |
Divide both sides by 3: | 24x = 192/3 = 64 | |
Rewrite in logarithmic form: | 4x = log2 64 | |
Evaluate: | 4x = 6 | |
Solve for x: | x = 6/4 = 1.5 |
Solution Method 2 (Taking the Log of Both Sides):
Write the equation: | 3(24x) = 192 | |
Take the log base 2 of both sides: | log2[3(24x)] = log2 192 | |
Use rule(1) Note this step!: | log2 3 + log2(24x) = log2 192 | |
Reorganize: | log2(24x) = log2 192 - log2 3 | |
Simplify right-hand side using rule (2): | log2(24x) = log2(192/3) = log264 = 6 | |
Use rule(3): | 4x log2 2 = 6 | |
Use rule(4): | 4x = 6 | |
Solve for x: | x =6/4 = 1.5 |
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