9^x + 9 = 10* 2^6x

Answer 1

To solve the equation 9^x + 9 = 10* 2^6x, we can rewrite the equation as:

3^(2x) + 9 = 10 * 2^6x

Then, we can further simplify the equation by converting everything into powers of 3:

3^(2x) + 3^2 = 3^1 * 2^(6x)

Now we can rewrite the equation as:

3^(2x) + 9 = 3 * 2^(6x)

Next, we can simplify this by noticing that 9 is equal to 3^2:

3^(2x) + 3^2 = 3 * 2^(6x)

Finally, we can rewrite the equation as:

3^(2x) + 3^(2) = 3 * 2^(6x)

Since both terms on the left-hand side are powers of 3, we can add them together:

3^(2x) + 3^(2) = 3 * 2^(6x)

3^(2x + 2) = 3 * 2^(6x)

Now, we can divide both sides by 3:

3^(2x + 2) / 3 = 2^(6x)

Simplify the left side:

3^2x * 3^2 / 3 = 2^(6x)

3^2 = 2^(6x)

9 = 2^(6x)

Now we can rewrite 9 as a power of 2:

2^3 = 2^(6x)

Since the bases are the same, we can equate the exponents:

3 = 6x

x = 3/6

x = 1/2

Therefore, the solution to the equation 9^x + 9 = 10* 2^6x is x = 1/2.