Solve

7^3x=623

take log base 7 of both sides:

3x = log7623
x = log7623 / 3

Now, you probably don;t have a log7 button on your calculator, so to make it so you can do it, change base:

x = 1/2 log623/log7

The nice thing is that now you can use any base you want. 10 or e, or even <gasp> 7! (Note that log77 = 1)

Okay so how would I calculate the answer from that step?

Eh? That IS the answer. log7 is a number, just like pi or √2.

Don't think you always have to resort to decimal numbers. If you must have that, just go to your favorite calculator, punch up log643, divide by log7, and divide by 3.

1.1076

You know that 7^3 = 343, so log7643 will be somewhere above 3. Divide by 3 and you have a number above 1.

Okay thanks. I think I got it now.

To solve the equation 7^(3x) = 623, we will take the logarithm of both sides of the equation to eliminate the exponent.

Step 1: Take the logarithm of both sides.
log(7^(3x)) = log(623)

Step 2: Apply the exponent property of logarithms.
(3x) * log(7) = log(623)

Step 3: Divide both sides by log(7) to isolate the variable.
3x = log(623) / log(7)

Step 4: Simplify the right side of the equation using a calculator.
3x ≈ 3.0778

Step 5: Divide both sides by 3 to solve for x.
x ≈ 1.0259

Therefore, the approximate solution to the equation 7^(3x) = 623 is x ≈ 1.0259.