# logarithms

Solve the following equations

3^x-2=6

Add 2 to both sides of the equation to start. Whatever operation you do to one side of an equation you must do to the other side as well.

3^x - 2 + 2 = 6 + 2

3^x = 8

Changing to logs:

log 3^x = log 8

x log 3 = log 8

x = log 8 / log 3

x = 1.8928 -->this is a rounded value.

This should check with the original equation.

I hope this helps.

## To solve the equation 3^x - 2 = 6, we can follow these steps:

Step 1: Add 2 to both sides of the equation.
3^x - 2 + 2 = 6 + 2
3^x = 8

Step 2: Take the logarithm of both sides. The logarithm function undoes exponentiation, so it allows us to find the value of x.
log(3^x) = log(8)

Step 3: Apply the logarithmic property log(a^b) = b * log(a).
x * log(3) = log(8)

Step 4: Divide both sides of the equation by log(3) to isolate x.
x = log(8) / log(3)

Step 5: Use a calculator to evaluate the logarithms.
x ≈ 1.8928 (rounded to 4 decimal places)

So, the solution to the equation 3^x - 2 = 6 is x ≈ 1.8928.