black3372809 black3372809
  • 17-02-2021
  • Mathematics
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Condense to a single logarithm : log 12 18+3 log 12 2

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mathstudent55
mathstudent55 mathstudent55
  • 17-02-2021

Answer:

2 or [tex] \log_{12} 144 [/tex]

Step-by-step explanation:

I assume 12 is the base.

[tex] \log_{12} 18 + 3 \log_{12} 2 = [/tex]

[tex] = \log_{12} 18 + \log_{12} 2^3 [/tex]

[tex] = \log_{12} (18 \times 8) [/tex]

[tex] = \log_{12} 144 [/tex]

[tex] = \log_{12} 12^2 [/tex]

[tex] = 2\log_{12} 12 [/tex]

[tex] = 2 [/tex]

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

[tex] \log_{12} 144 [/tex]

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