Log Equations

Most calculators evaluate logs with base 10.

Evaluate $$\log_{11}4$$ on the calculator.

Name the following log property: $$\log_b\left(mn\right)=\log_bm+\log_bn$$ .

Solve the following log equation:

$$\log\left(x+2\right)=\log\left(-2x+5\right)$$

Name the following log property:

$$\log_b\left(\frac{m}{n}\right)=\log_bm-\log_bn$$

Use log properties and log loop to solve for x:

$$\log\left(x\right)-\log\left(2\right)=1$$

Name the following log property:

$$\log_bm^n=n\log_bm$$

Solve for x: $$\log_2\left(3x-4\right)=\log_2\left(-2x+6\right)$$

Find the missing numbers that make the equation true:

$$\log\left(?\right)+\log\left(?\right)=\log\left(24\right)$$

Solve for x: $$\log\left(2x\right)+\log\left(3\right)=\log\left(12\right)$$