91Ó°ÊÓ

Solve the logarithmic equations. Round your answers to three decimal places. $$\log _{7}(1-x)-\log _{7}(x+2)=\log _{7} x$$

Solve the logarithmic equations. Round your answers to three decimal places. $$\log _{5}(x+1)-\log _{5}(x-1)=\log _{5} x$$

If \(\$ 5,000\) is invested in a savings account that earns \(3 \%\) interest compounding continuously, how much will be in the account in 6 months? Solution: Write the compound continuous interest formula. \(\quad A=P e^{r t}\) Substitute \(P=5000, r=0.03,\) and \(t=6 . \quad A=5000 e^{(0.03)(6)}\) Simplify. \(A=5986.09\) This is incorrect. What mistake was made?

Simplify if possible and explain the mistake that is made. \(\ln 3+2 \ln 4-3 \ln 2\) Solution: Apply the power property (7) $$\ln 3+\ln 4^{2}-\ln 2^{3}$$ Simplify. $$\ln 3+\ln 16-\ln 8$$ Apply property (5) $$\ln (3+16-8)$$ Simplify. $$\ln 11$$ This is incorrect. The correct answer is \(\ln 6 .\) What mistake was made?

Determine whether each statement is true or false. The function \(f(x)=-e^{-x}\) has the \(y\) -intercept (0,1)

Simplify if possible and explain the mistake that is made. \(\log _{2} x+\log _{3} y-\log _{4} z\) Solution: Apply the product property (5) $$\log _{6} x y-\log _{4} z$$ Apply the quotient property (6) $$\log _{24} x y z$$ This is incorrect. What mistake was made?

Solve the logarithmic equations. Round your answers to three decimal places. $$\ln \sqrt{x+4}-\ln \sqrt{x-2}=\ln \sqrt{x+1}$$

Determine whether each statement is true or false. The function \(f(x)=-e^{-x}\) has a horizontal asymptote along the \(x\) -axis.

Solve the logarithmic equations. Round your answers to three decimal places. $$\log (\sqrt{1-x})-\log (\sqrt{x+2})=\log x$$

Determine whether each statement is true or false. $$\log e=\frac{1}{\ln 10}$$