Question

Solve each equation for x.
e⁹ − ⁴ˣ = 6

Answer 1

To solve the equation e⁹ − ⁴ˣ = 6, take the natural logarithm of both sides to isolate x, then rearrange the equation and apply logarithmic properties to solve for x.

Step-by-step explanation:

To solve the equation e⁹ − ⁴ˣ = 6, we can take the natural logarithm (ln) of both sides. This will help us isolate the exponent x. Here are the steps:

1. Take the natural logarithm of both sides: ln(e⁹ − ⁴ˣ) = ln(6).
2. Use the logarithmic property to bring down the exponent: 9 - ⁴ˣ * ln(e) = ln(6).
3. Since ln(e) equals 1, we simplify further: 9 - ⁴ˣ = ln(6).
4. Move ⁴ˣ to the left side by subtracting it from both sides: 9 = ⁴ˣ + ln(6).
5. Now, we can solve for x by subtracting ln(6) from both sides and rearranging the equation: ⁴ˣ = 9 - ln(6).
6. Finally, take the logarithm (log) base 4 of both sides to solve for x: x = log base 4(9 - ln(6)).