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stiv31 [10]
3 years ago
9

(1/27)^x-6=27Could I please have a step by step as well? Much appreciated! ​

Mathematics
1 answer:
Andrei [34K]3 years ago
5 0

Answer:

x = 7

Step-by-step explanation:

1) Use Division Distributive Property: (x/y)^a = x^a/y^a.

\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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