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zysi [14]
3 years ago
10

What is the true solution to 3 In 2+In 8 = 2 In(4x)? 60f Š O OOO TNT 00

Mathematics
1 answer:
alina1380 [7]3 years ago
4 0

Answer:

  x = 2

Step-by-step explanation:

Taking antilogs, you have ...

  2³ × 8 = (4x)²

  64 = 16x²

  x = √(64/16) = √4

  x = 2 . . . . . . . . (the negative square root is not a solution)

___

You can also work more directly with the logs, if you like.

  3·ln(2) +ln(2³) = 2ln(2²x) . . . . . . . . . . . write 4 and 8 as powers of 2

  3·ln(2) +3·ln(2) = 2(2·ln(2) +ln(x)) . . . . use rules of logs to move exponents

  6·ln(2) = 4·ln(2) +2·ln(x) . . . . . . . . . . . . simplify

  2·ln(2) = 2·ln(x) . . . . . . . . . . . subtract 4ln(2)

  ln(2) = ln(x) . . . . . . . . . . . . . . divide by 2

  2 = x . . . . . . . . . . . . . . . . . . . take the antilogs

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Step-by-step explanation:

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3 years ago
convert 13542 base six to base ten. I'm in math20 at Folsom Lake College and i'm trying to figure out this question. I had most
VikaD [51]
Converting to base 10 can be done easily by writing a sort of digit expansion. In base 6, this number literally means

13542_6=1\times6^4+3\times6^3+5\times6^2+4\times6^1+2\times6^0

Simplifying this gives the value in base 10.

13542_6=1296+3\times216+5\times36+4\times6+2
13542_6=2150_{10}
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