The exponential equation 3^x=12 does not have an integer solution. Use an over/under table to find an estimate of the solution to two decimal places. You can also write as a logarithm and evaluate in your calculator.
4.12
3.16
2.26
To get started, let's rewrite the equation 3^x = 12 as a logarithmic equation.
Taking the logarithm of both sides gives us:
x = log3(12)
Now let's evaluate log3(12) using a calculator:
log3(12) ≈ 2.26185950714
Therefore, the estimate of the solution to two decimal places is x ≈ 2.26.
Using an over/under table:
3^2 = 9 (under)
3^3 = 27 (over)
This also indicates that the solution is between 2 and 3, further confirming our estimate of x ≈ 2.26.