Laws of logarithms

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Mathematics

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52x-3 = 1 et2 5 = 1 Ee Spera x = +3 52x-3=5° 2x - 30 X = Method 2: Use logarithms to solve exponential equations using: logp M = logh N M= N Find EXACT and APPROXIMATE answers for these problems. Round your answers to 6 decimals. Example: 32x-1 = 5 let M = 32x-1 and N = 5 1. Take the log or In of both sides: log(32x-1) = log(5) 2. Use the Power Law: (2x - 1) log(3) = log(5) 3. Divide both sides by log(3), so then log(5) 2x – 1= log(3) 4. Add 1 to both sides, so then log(5) 2x - 1 + 1 = +1 becomes log(3) log(5) 2x = +1 log(3) 5. Divide both sides by 2 (or multiply by y) X = 11.99 + 1] THIS IS THE EXACT ANSWER 2 Llog(3) x = 1.232487 approximate answer rounded to 6 decimal places 4(1 + 105x) = 9 Isolate the "x" term first, before taking the log of both sides. eso 4* + 21+2x = 50 GUIDELINES FOR SOLVING LOGARITHMIC EQUATIONS 1. Isolate the logarithmic term on one side of the equation; you might first need to combine the logarithmic terms. 2. Write the equation in exponential form (or raise the base to each side of the equation). 3. Solve for the variable. CHECK ANSWERS: LOGS CANNOT BE NEGATIVE log(x) + log(x + 1) = log(4x) 2logs x = logs 2 + logs (3x - 4) 1- logz(x2 - x - 2) = 2 Use the definition loga(x) = y ay = x D log)(x + 1) - log5(x - 1) = 2 log(x) + log(x - 3) = 1 log4(x + 2) + log4(3) = log4(5) + log4(2x - 3)
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