Question

Solve for x 3^x+4=9 3 to the power of x plus 4 is equal to 9

Answer 1

$3^{x} + 4 = 9 \\3^{x} = 5 \\ln(3^{x}) = ln(5) \\xln(3) = ln(5) \\\frac{xln(3)}{ln(3)} = \frac{ln(5)}{ln(3)} \\x = \frac{ln(5)}{ln(3)}$

or

$3^{x + 4} = 9 \\ln(3^{x + 4}) = ln(9) \\(x + 4)ln(3) = ln(9) \\\frac{(x + 4)ln(3)}{ln(3)} = \frac{ln(9)}{ln(3)} \\x + 4 = \frac{ln(3^{2})}{ln(3)} \\x + 4 = \frac{2ln(3)}{ln(3)} \\x + 4 = 2 \\x = -2$

Answer 2

3^x + 4 = 9
Subtract 4 from both sides:
3^x = 5
Now, take the logarithm base 3 of both sides:
x = log(5)/log(3)
If you solve for x, you should end up with approximately 1.4650