Calculus Examples

$10^{3 - x} = 1$

Step 1

Take the base $10$ logarithm of both sides of the equation to remove the variable from the exponent.

$\log (10^{3 - x}) = \log (1)$

Step 2

Expand the left side.

Tap for more steps...

Step 2.1

Expand $\log (10^{3 - x})$ by moving $3 - x$ outside the logarithm.

$(3 - x) \log (10) = \log (1)$

Step 2.2

Logarithm base $10$ of $10$ is $1$ .

$(3 - x) \cdot 1 = \log (1)$

Step 2.3

Multiply $3 - x$ by $1$ .

$3 - x = \log (1)$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Logarithm base $10$ of $1$ is $0$ .

$3 - x = 0$

Step 4

Subtract $3$ from both sides of the equation.

$- x = - 3$

Step 5

Divide each term in $- x = - 3$ by $- 1$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $- x = - 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 3}{- 1}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 3}{- 1}$

Step 5.2.2

Divide $x$ by $1$ .

$x = \frac{- 3}{- 1}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Divide $- 3$ by $- 1$ .

$x = 3$