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Mathematics, 17.09.2019 05:00 hayleegreenwell34
Let x, y, and z be positive real numbers that satisfy\[2 \log_x (2y) = 2 \log_{2x} (4z) = \log_{2x^4} (8yz) \neq 0.\]the value of xy^5 z can be expressed in the form \frac{1}{2^{p/q}}, where p and q are relatively prime positive integers. find p + q.
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Answers: 3
![ansver](/tpl/images/cats/User.png)
Answer from: Quest
use the power rule
( a b ) n = a n b n
to distribute the exponent.
apply the product rule to
3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2
apply the product rule to
3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2
raise
3
to the power of
2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in ( x 2 ) 2
.
apply the power rule and multiply exponents,
( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2
multiply
2 by 2 . 9 x 4 ( y 3 ) 2
multiply the exponents in
( y 3 ) 2 .
apply the power rule and multiply exponents,
( a m ) n = a m n . 9 x 4 y 3
⋅
2
multiply
3 by 2 . 9 x 4 y 6
step-by-step explanation:
![ansver](/tpl/images/cats/User.png)
Answer from: Quest
answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality
step-by-step explanation:
![ansver](/tpl/images/cats/User.png)
Answer from: Quest
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Let x, y, and z be positive real numbers that satisfy\[2 \log_x (2y) = 2 \log_{2x} (4z) = \log_{2x^4...
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