Question

10^x +10^y = 10 .find the domain

Answer 1

here is you solution.....
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${10}^{x} + {10}^{y} = 10 \\ x + {10}^{y} = \frac{10}{10} \\ x + {10}^{y} = 1$
$x + y = \frac{1}{10} \\ x + y = 0.1$

<==== ANSWER ====>
X = 0.1 - y
Y = 0.1 - x

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Answer 2

Answer:

The domain of the given function is all real numbers less than 1, i.e., (-∞,1).

Step-by-step explanation:

The given function is

$10^x+10^y=10$

Isolate the variable y.

$10^y=10-10^x$

Taking log on both the sides.

$log(10^y)=log(10-10^x)$

$y=log(10-10^x)$                   $[\because log10^a=a]$

The logistic function is defined for non zero positive real numbers.

$10-10^x>0$

$10>10^x$

Since base is same, so we get

$1>x$

Therefore the domain of the given function is all real numbers less than 1, i.e., (-∞,1).