Basic Math Examples

$3^{a} + 7^{b} = 1029$

Step 1

Subtract $7^{b}$ from both sides of the equation.

$3^{a} = 1029 - 7^{b}$

Step 2

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

$\ln (3^{a}) = \ln (1029 - 7^{b})$

Step 3

Expand $\ln (3^{a})$ by moving $a$ outside the logarithm.

$a \ln (3) = \ln (1029 - 7^{b})$

Step 4

Divide each term in $a \ln (3) = \ln (1029 - 7^{b})$ by $\ln (3)$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $a \ln (3) = \ln (1029 - 7^{b})$ by $\ln (3)$ .

$\frac{a \ln (3)}{\ln (3)} = \frac{\ln (1029 - 7^{b})}{\ln (3)}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $\ln (3)$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{a \ln (3)}{\ln (3)} = \frac{\ln (1029 - 7^{b})}{\ln (3)}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{\ln (1029 - 7^{b})}{\ln (3)}$