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DaniilM [7]
3 years ago
10

Condense to a single logarithm : log 12 18+3 log 12 2

Mathematics
1 answer:
Over [174]3 years ago
8 0

Answer:

2 or \log_{12} 144

Step-by-step explanation:

I assume 12 is the base.

\log_{12} 18 + 3 \log_{12} 2 =

= \log_{12} 18 + \log_{12} 2^3

= \log_{12} (18 \times 8)

= \log_{12} 144

= \log_{12} 12^2

= 2\log_{12} 12

= 2

The entire expression simplifies to 2, but if you need the simplest log expression, then you can use

\log_{12} 144

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The main reason to know the multiplication table is so you can more easily multiply larger numbers. For example, suppose you want to multiply 53 x 7. Start by stacking these numbers on top of another, aligning the ones place. Draw a line underneath, and then multiply 3 by 7. Because 3 x 7 = 21, write down the ones digit (1) and carry the tens digit (2) to the tens column:

Next, multiply 5 by 7. This time, 5 x 7 = 35. But you also need to add the 2 that you carried over, which makes the result 37. Because 5 and 7 are the last numbers to multiply, you don’t have to carry, so write down the 37 — you find that 53 x 7 = 371:

When multiplying larger numbers, the idea is similar. For example, suppose you want to multiply 53 by 47. Be sure to align the stacked numbers by the ones place. (The first few steps — multiplying by the 7 in 47 — are the same, so pick up the next step.) Now you’re ready to multiply by the 4 in 47. But remember that this 4 is in the tens column, so it really means 40. So to begin, put a 0 directly under the 1 in 371:

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When multiplying by larger numbers with two digits or more, use one placeholding zero when multiplying by the tens digit, two placeholding zeros when multiplying by the hundreds digit

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