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Sums and Differences. Condensing Logs. Condensing Logs. Last time we expanded logs, today we will reverse the order. We will still be using rules 5, 6, and 7. When condensing logs it is important to remember 2 things: 1. The bases must be the same. 2. You will only write “log” one time.
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Sums and Differences Condensing Logs
Condensing Logs • Last time we expanded logs, today we will reverse the order. • We will still be using rules 5, 6, and 7. • When condensing logs it is important to remember 2 things: • 1. The bases must be the same. • 2. You will only write “log” one time.
Condensing Logs The bases are the same, so combine into one log by multiplying. Bring the numbers in front up as powers. (rule 7) Then combine as one log by multiplying. • log5x + log5y • log5xy • 3log2x + 4log2y • log2x3 + log2y4 • log2x3y4
Condensing logs Bases are the same, so combine as a division problem. Bring the numbers in the front back as powers. Condense into one log using division. • log38 – log37 • log3() • 2log2x – 3log2y • log2x2 – log2y3 • log2()
Condensing Logs • Put it all together now! • 3log5x + 2log5y – 3log5q • log5x3 + log5y2 – log5q3 • log5
Condensing logs • Here is a hard one…. • 3log3x + 2log3y – 5log3z - 4log3q • log3x3 + log3y2 – log3z5 – log3q4 • log3x3 + log3y2 – (log3z5 + log3q4) • log3
Condensing Logs • Helpful hints….. • Take each problem step by step. • Take care of numbers in the front first, then worry about addition and subtraction. • Double check your final answer and make sure there is only one “log”.
