SOLUTION: pls help me out found dis question in a txt book a logarithm simultaenous eqn 2logbasex of y+2logbase x of y=5 ;xy=27

Question 1063440: pls help me out found dis question in a txt book a logarithm simultaenous eqn
2logbasex of y+2logbase x of y=5 ;xy=27
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
(2 * log(x) y) + (2 * log(x) y) = 5 and x * y = 7
:
use the power rule log(b) (x^y) = y ∙ log(b) (x)
:
log(x) y^2 + log(x) y^2 = 5
:
use the product rule log(b) (x * y) = log(b) (x) + log(b) (y)
:
log(x) y^4 = 5
:
use definition of logarithm
:
y^4 = x^5
:
use y = 7 / x and substitute for y
:
(7 / x)^4 = x^5
:
2401 / x^4 = x^5
:
x^9 = 2401
:
***********************
x = 2401^(1/9) = 2.3746
y = 7 / 2.3746 = 2.9479
***********************
:
check answers
:
(2 * log(2.3746) 2.9479) + (2 * log(2.3746) 2.9479) = 5
:
(2 * 1.25) + 2 * 1.25) = 5
:
2.50 + 2.50 = 5
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5 = 5
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our answer checks
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