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Ipatiy [6.2K]
4 years ago
13

4 to the 8th power divided by 4 to the 5th power

Mathematics
1 answer:
Natasha2012 [34]4 years ago
6 0

Alright, 4 to the 8th power is 4x4x4x4x4x4x4x4 which ends up as 65,536.

4 to the 5th power is the same thing but with 5 4's and that is 1,024.

All you need to do now is 65,536/1,024 = 64.

Solved!  :D

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Step-by-step explanation:

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\frac{1}{ {27}^{x - 8} }  = 27

2) Multiply both sides by 27^x - 8.

1 =  {27} \times 27^{1 + x  - 8}

3) Use the product rule: x^a x^b = x^a+b.

1 =  {27}^{1 + x - 8}

4) Simplify 1 + x - 8 to x - 7.

1  =  {27}^{x - 7}

5) Use Definition of Common Logarithm: b^a = x if and only if log<u>b</u><u> </u>(x) = a.

log_{27}1 = x - 7

6) Use Change of Base Rule.

\frac{ log_1  }{  log{27} }  = x - 7

7) Use rule of 1: log 1 = 0.

\frac{0}{ log_{27}}  = x - 7

8) Simplify 0/log_27 to 0.

0 = x - 7

9) Add 7 to both sides.

7 = x

10) Switch sides.

x = 7

<u>Therefor</u><u>,</u><u> </u><u>the</u><u> </u><u>answer</u><u> </u><u>is</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>7</u><u>.</u>

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