9^x + 9 = 10* 2^6

Answer 1

To solve for x in the equation 9^x + 9 = 10* 2^6, we first simplify the right side of the equation:

10*2^6 = 10*64
10*64 = 640

Now, the equation becomes:

9^x + 9 = 640

Subtracting 9 from both sides, we get:

9^x = 631

Now, we need to find the value of x that satisfies this equation. We can start by expressing 631 as a power of 9:

9^3 = 729
9^4 = 6561

Since 631 is between 729 and 6561, we know that x is between 3 and 4. To find the exact value of x, we can take the logarithm of both sides:

log(9^x) = log(631)
x*log(9) = log(631)
x = log(631)/log(9)

Using a calculator, we find:

x ≈ 3.545

Therefore, x is approximately 3.545.