Finite Math Examples

$5^{x} = 10^{c (x)}$

Step 1

Take the log of both sides of the equation.

$\ln (5^{x}) = \ln (10^{c (x)})$

Step 2

Expand $\ln (5^{x})$ by moving $x$ outside the logarithm.

$x \ln (5) = \ln (10^{c (x)})$

Step 3

Expand $\ln (10^{c (x)})$ by moving $c (x)$ outside the logarithm.

$x \ln (5) = c (x) \ln (10)$

Step 4

Multiply $c$ by $x$ .

$x \ln (5) = c x \ln (10)$

Step 5

Solve the equation for $x$ .

Tap for more steps...

Step 5.1

Subtract $c x \ln (10)$ from both sides of the equation.

$x \ln (5) - c x \ln (10) = 0$

Step 5.2

Factor $x$ out of $x \ln (5) - c x \ln (10)$ .

Tap for more steps...

Step 5.2.1

Factor $x$ out of $x \ln (5)$ .

$x (\ln (5)) - c x \ln (10) = 0$

Step 5.2.2

Factor $x$ out of $- c x \ln (10)$ .

$x (\ln (5)) + x (- c \ln (10)) = 0$

Step 5.2.3

Factor $x$ out of $x (\ln (5)) + x (- c \ln (10))$ .

$x (\ln (5) - c \ln (10)) = 0$

Step 5.3

Divide each term in $x (\ln (5) - c \ln (10)) = 0$ by $\ln (5) - c \ln (10)$ and simplify.

Tap for more steps...

Step 5.3.1

Divide each term in $x (\ln (5) - c \ln (10)) = 0$ by $\ln (5) - c \ln (10)$ .

$\frac{x (\ln (5) - c \ln (10))}{\ln (5) - c \ln (10)} = \frac{0}{\ln (5) - c \ln (10)}$

Step 5.3.2

Simplify the left side.

Tap for more steps...

Step 5.3.2.1

Cancel the common factor of $\ln (5) - c \ln (10)$ .

Tap for more steps...

Step 5.3.2.1.1

Cancel the common factor.

$\frac{x (\ln (5) - c \ln (10))}{\ln (5) - c \ln (10)} = \frac{0}{\ln (5) - c \ln (10)}$

Step 5.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{\ln (5) - c \ln (10)}$

Step 5.3.3

Simplify the right side.

Tap for more steps...

Step 5.3.3.1

Divide $0$ by $\ln (5) - c \ln (10)$ .

$x = 0$