Pre-Algebra Examples

$n = \frac{12.34}{0.04 + 58^{t}}$

Step 1

Rewrite the equation as $\frac{12.34}{0.04 + 58^{t}} = n$ .

$\frac{12.34}{0.04 + 58^{t}} = n$

Step 2

Multiply both sides by $0.04 + 58^{t}$ .

$\frac{12.34}{0.04 + 58^{t}} (0.04 + 58^{t}) = n (0.04 + 58^{t})$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Cancel the common factor of $0.04 + 58^{t}$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

$\frac{12.34}{0.04 + 58^{t}} (0.04 + 58^{t}) = n (0.04 + 58^{t})$

Step 3.1.1.2

Rewrite the expression.

$12.34 = n (0.04 + 58^{t})$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $n (0.04 + 58^{t})$ .

Tap for more steps...

Step 3.2.1.1

Apply the distributive property.

$12.34 = n \cdot 0.04 + n \cdot 58^{t}$

Step 3.2.1.2

Simplify the expression.

Tap for more steps...

Step 3.2.1.2.1

Move $0.04$ to the left of $n$ .

$12.34 = 0.04 \cdot n + n \cdot 58^{t}$

Step 3.2.1.2.2

Reorder $n$ and $58^{t}$ .

$12.34 = 0.04 n + 58^{t} \cdot n$

Step 4

Solve for $t$ .

Tap for more steps...

Step 4.1

Rewrite the equation as $0.04 n + 58^{t} \cdot n = 12.34$ .

$0.04 n + 58^{t} \cdot n = 12.34$

Step 4.2

Reorder factors in $0.04 n + 58^{t} n$ .

$0.04 n + n \cdot 58^{t} = 12.34$

Step 4.3

Subtract $0.04 n$ from both sides of the equation.

$n \cdot 58^{t} = 12.34 - 0.04 n$

Step 4.4

Divide each term in $n \cdot 58^{t} = 12.34 - 0.04 n$ by $n$ and simplify.

Tap for more steps...

Step 4.4.1

Divide each term in $n \cdot 58^{t} = 12.34 - 0.04 n$ by $n$ .

$\frac{n \cdot 58^{t}}{n} = \frac{12.34}{n} + \frac{- 0.04 n}{n}$

Step 4.4.2

Simplify the left side.

Tap for more steps...

Step 4.4.2.1

Cancel the common factor of $n$ .

Tap for more steps...

Step 4.4.2.1.1

Cancel the common factor.

$\frac{n \cdot 58^{t}}{n} = \frac{12.34}{n} + \frac{- 0.04 n}{n}$

Step 4.4.2.1.2

Divide $58^{t}$ by $1$ .

$58^{t} = \frac{12.34}{n} + \frac{- 0.04 n}{n}$

Step 4.4.3

Simplify the right side.

Tap for more steps...

Step 4.4.3.1

Cancel the common factor of $n$ .

Tap for more steps...

Step 4.4.3.1.1

Cancel the common factor.

$58^{t} = \frac{12.34}{n} + \frac{- 0.04 n}{n}$

Step 4.4.3.1.2

Divide $- 0.04$ by $1$ .

$58^{t} = \frac{12.34}{n} - 0.04$

Step 4.5

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

$\ln (58^{t}) = \ln (\frac{12.34}{n} - 0.04)$

Step 4.6

Expand $\ln (58^{t})$ by moving $t$ outside the logarithm.

$t \ln (58) = \ln (\frac{12.34}{n} - 0.04)$

Step 4.7

Divide each term in $t \ln (58) = \ln (\frac{12.34}{n} - 0.04)$ by $\ln (58)$ and simplify.

Tap for more steps...

Step 4.7.1

Divide each term in $t \ln (58) = \ln (\frac{12.34}{n} - 0.04)$ by $\ln (58)$ .

$\frac{t \ln (58)}{\ln (58)} = \frac{\ln (\frac{12.34}{n} - 0.04)}{\ln (58)}$

Step 4.7.2

Simplify the left side.

Tap for more steps...

Step 4.7.2.1

Cancel the common factor of $\ln (58)$ .

Tap for more steps...

Step 4.7.2.1.1

Cancel the common factor.

$\frac{t \ln (58)}{\ln (58)} = \frac{\ln (\frac{12.34}{n} - 0.04)}{\ln (58)}$

Step 4.7.2.1.2

Divide $t$ by $1$ .

$t = \frac{\ln (\frac{12.34}{n} - 0.04)}{\ln (58)}$