precalc

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1.Solve the equation algebraically. Round the result to three decimal places. Verify your answer using a graphing utility.

3 − ln x

= 0

2.Consider the following.

5 log10(x − 6) = 11

(a) Complete the table to find an interval containing the solution of the equation. Round your results to three decimal places.

x	150	155	160	165	170
5 log10(x − 6)

What is the smallest open interval based on the table above that contains the solution of the equation? (Use the x-values given by the table.) (b) Use a graphing utility to graph both sides of the equation to estimate the solution. Round your result to three decimal places. x = (c) Solve the equation algebraically. Round your result to three decimal places. x =

3. Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If there is no solution, enter NO SOLUTION.)

ln(x + 3) – ln(x – 3) = ln(x)

4. Solve the logarithmic equation algebraically. Round the result to three decimal places. Verify your answer using a graphing utility. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

3 + 4 ln x = 12

5. Simplify the expression.

${\color{red}-9} + e^{\ln x^{{\color{red}9}}}$

6. Simplify the expression.

$e^{\ln(x^{{\color{red}2}} + {\color{red}4})}$

7. Solve the logarithmic equation. (Round your answer to three decimal places.)

ln(6x + 3) = 4