2.13 - Exponential and Logarithmic Equations and Inequalities

Let $$f\left(x\right)=\log_3\left(x^2+x+2\right)-\log_3\left(x+6\right).$$ What are all the values of x for which $$f\left(x\right)<0?$$

(a)  

Let $$h\left(x\right)=\ln\left(x^2+5\right)$$ and let $$k\left(x\right)=\ln\left(7x-7\right)$$ . What are all values of x for which $$h\left(x\right)>k\left(x\right)?$$

Let $$p\left(x\right)=12+5\left(3\right)^{4x+1}$$ . What are all values for which $$p\left(x\right)\ge57?$$

$$2^{x+3}+5>37$$

Solve. Write solutions in INEQUALITY notation.

$$\log5+\log\left(x-2\right)\ge\log\left(3x+8\right)$$

Solve. Write solutions in INEQUALITY notation.

$$\log_2\left(x+5\right)-8>-3$$

Solve. Write solutions in INEQUALITY notation.

What are the solutions to the inequality?

$$\log\left(x-3\right)+\log\left(5\right)>\log\left(x+9\right)$$

What are the solutions to the inequality?

$$\ln\left(x+4\right)\le\ln\left(x-6\right)+\ln3$$

Solve. Write solutions in INEQUALITY notation.

$$4\left(3^{2x}\right)-8\le316$$

$$\log_4x<3$$

(a)