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Anni [7]
3 years ago
5

Changing Bases to Evaluate Logarithms In Exercise, use the change-of-base formula and a calculator to evaluate the logarithm.

Mathematics
1 answer:
Ymorist [56]3 years ago
3 0

Answer:

\frac{3}{2}

Step-by-step explanation:

Changing Bases to Evaluate Logarithms

log_{16}(64)

Apply change of base formula'

log_b(a)= \frac{log a}{log b}

log term should be the numerator and denominator is the log base

log_{16}(64)

log_{16}(a)= \frac{log 64}{log 16}

64 is 4^3  and 16 is 4^2

log_{16}(a)= \frac{log 4^3}{log 4^2}

Move the exponent before log

\frac{3log 4}{2log 4}

top and bottom has same log so cancel it out

\frac{3}{2}

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Questio
Olenka [21]

Answer:

  d = -1/3, 0

Step-by-step explanation:

Subtract the constant on the left, take the square root, and solve from there.

  (6d +1)^2 + 12 = 13 . . . . given

  (6d +1)^2 = 1 . . . . . . . . . .subtract 12

  6d +1 = ±√1 . . . . . . . . . . take the square root

  6d = -1 ±1 . . . . . . . . . . . .subtract 1

  d = (-1 ±1)/6 . . . . . . . . . . divide by 6

  d = -1/3, 0

_____

Using a graphing calculator, it is often convenient to write the function so the solutions are at x-intercepts. Here, we can do that by subtracting 13 from both sides:

  f(x) = (6x+1)^ +12 -13

We want to solve this for f(x)=0. The solutions are -1/3 and 0, as above.

4 0
3 years ago
Katie gives Maggie half of her pencils. Maggie keeps 5 and gives the rest to jamil. Write an expression for the number of pencil
Inga [223]

Answer

Write an expression for the number of pencils Maggie gives to jamil.

To prove

Let us assume that the number of pencils Katie have = x

As given

Katie gives Maggie half of her pencils.

Katie\ gives\ Maggie\ half\ of\ her\ pencils = \frac{1x}{2}

As given

Maggie keeps 5 and gives the rest to jamil.

Thus

Number\ of\ pencils\ Maggie\ gives\ to\ jamil = \frac{1x}{2} - 5

Therefore the expression for the number of pencils Maggie gives to jamil are  \frac{1x}{2} - 5.





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