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.