Using the change-of-base formula, which of the following is equivalent to the

Mathematics

1 answer:

tamaranim1 [39]2 years ago

5 0

Answer:

See below

Step-by-step explanation:

There could be INFINITE possibilities....(you didn't list any choices to choose from)

here is one to change to base 10

log5 ( 13) = log10 ( 13) / log10 ( 5)

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Answer:

$\frac{511\,\,\sqrt{3} }{99}$ which is an irrational number

Step-by-step explanation:

Recall that the repeating decimal 0.7373737373... can be written in fraction form as: $\frac{73}{99}$

Now, let's write the number 147 which is inside the square root in factor form to find if it has some perfect square factors:

$147=7^2\,3$

Then, 7 will be able to go outside the root when we compute the final product requested:

$\frac{73}{99} \,*\,7\,\sqrt{3} =\frac{511\,\,\sqrt{3} }{99}$

This is an irrational number due to the fact that it is the product of a rational number (quotient between 511 and 99) times the irrational number $\sqrt{3}$