solve the equation. give an exact solution, and also an approximate solution to four decimal places.

2^(9x-7)=7

My first step was to change it to
log(base 2) 7 = 9x-7
i got 1.0897
Did i do something wrong or did i miss one question?

just take log of both sides

log (2^(9x-7)) = log 7
(9x-7) log2 = log7
9x - 7 = log7/log2
etc.

your answer is correct, see

http://www.google.ca/search?hl=en&source=hp&q=%28%28log%287%29%2Flog%282%29%2B7%29%2F9&btnG=Google+Search&aq=f&aqi=&aql=&oq=

[9x -7] log 2 = log 7

Any log base can be used, as long as it is the same for both sides.
9x - 7 = 2.807
9x = 9.807
x = 1.0897

Your answer is correct!

It seems like you made a calculation error when solving the equation. Let's go through the steps again to find the correct solution.

Starting with the equation:
2^(9x - 7) = 7

First, we want to isolate the exponential term by taking the logarithm of both sides of the equation. Since the base is 2, we will use logarithm base 2 (log2) to simplify the equation.

log2(2^(9x - 7)) = log2(7)

Using the property of logarithms, the exponent can be brought down as a coefficient:

(9x - 7)log2(2) = log2(7)

Since log2(2) is equal to 1, the equation becomes:

9x - 7 = log2(7)

Next, we want to isolate the variable x. We can achieve this by adding 7 to both sides of the equation:

9x - 7 + 7 = log2(7) + 7

Simplifying further:

9x = log2(7) + 7

Now, divide both sides of the equation by 9 to solve for x:

x = (log2(7) + 7) / 9

To find an exact solution, we can leave the equation in this form. However, if you want an approximate solution to four decimal places, you can substitute the value of log2(7) into the equation and perform the calculation:

x ≈ (log2(7) + 7) / 9 ≈ (2.80735 + 7) / 9 ≈ 9.80735 / 9 ≈ 1.0897 (rounded to four decimal places)

Therefore, the approximate solution to four decimal places is x ≈ 1.0897.

Just remember to be careful with your calculations to avoid errors in the future.