Linear Algebra Examples

$\log_{2} (x + 5) - \log ({(2)}^{x}) = 3$

Step 1

Set the argument in $\log_{2} (x + 5)$ greater than $0$ to find where the expression is defined.

$x + 5 > 0$

Step 2

Subtract $5$ from both sides of the inequality.

$x > - 5$

Step 3

Set the argument in $\log ({(2)}^{x})$ greater than $0$ to find where the expression is defined.

${(2)}^{x} > 0$

Step 4

Solve for $x$ .

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Step 4.1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (2^{x}) > \ln (0)$

Step 4.2

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

Step 4.3

There is no solution for $2^{x} > 0$

No solution

Step 5

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- 5, \infty)$

Set-Builder Notation:

${x | x > - 5}$

Step 6