Need help with current Trig problem for tomorrow:
Solve the logarithmic equation algebraically. Approximate the result to three decimal places.
6log3(0.5x)=11
I know to start off the equation you divide by 6.
I know the answer is 14.988. I just am puzzled on how to receive the answer.
6log3(0.5x)=11
log3 (.5x) = 11/6
3^[log3 (.5x)] = .5 x = 3^(11/6)
x = 2 * 3^(11/6)
x = 2 * 4.494
x = 14.9882972
To solve the logarithmic equation, follow these steps:
Step 1: Divide both sides of the equation by 6 to isolate the logarithm:
log3(0.5x) = 11/6
Step 2: Convert the logarithmic equation into exponential form:
3^(log3(0.5x)) = 3^(11/6)
Step 3: Simplify the left side using the logarithmic property:
0.5x = 3^(11/6)
Step 4: Solve for x by taking the logarithm again:
x = (log(3^(11/6)))/log(0.5)
Step 5: Use a calculator to evaluate the logarithms and calculate the value of x.
x ā 14.988
Therefore, the solution to the logarithmic equation is x ā 14.988 (rounded to three decimal places).