Question

Log7(9+3x)=2 log2(7+3x)=3 log3(14-x)=2 Help

Answer 1

Ответ:

g=2 log 7 (10) -3x, x € R

x=log 2 (10)-7-3

x=-2H+14 H €R

Answer 2

To solve these logarithmic equations, we'll follow the steps for each equation:

1. Log7(9+3x) = 2

Step 1: Rewrite the equation in exponential form: 7^2 = 9 + 3x

Step 2: Solve for x: 49 = 9 + 3x 3x = 40 x = 40/3

2. Log2(7+3x) = 3

Step 1: Rewrite the equation in exponential form: 2^3 = 7 + 3x

Step 2: Solve for x: 8 = 7 + 3x 3x = 8 - 7 3x = 1 x = 1/3

3. Log3(14-x) = 2

Step 1: Rewrite the equation in exponential form: 3^2 = 14 - x

Step 2: Solve for x: 9 = 14 - x x = 14 - 9 x = 5

So, the solutions to the equations are: x = 40/3, x = 1/3, and x = 5.