Question

Solve the equation for x. show your work log(2x-6)=2

Answer 1

x = 53

Explanation:

Rewrite log ( 2 x − 6 ) = 2 in exponential form using the definition of a logarithm. If x and b are positive real numbers and b ≠ 1 , then log b ( x ) = y is equivalent to b y = x .

10 = x − 6

Solve for x .

Rewrite the equation as

x − 6 = 10 .

x − 6 = 10

Raise 10 to the power of 2 .

x − 6 = 100

Move all terms not containing x to the right side of the equation.

x = 106

Divide each term by 2 and simplify. x = 53

Answer 2

x = e^2/2 + 3

Explanation:

Solve for x:

log(2 x - 6) = 2

Hint: | Eliminate the logarithm from the left hand side.

Cancel logarithms by taking exp of both sides:

2 x - 6 = e^2

Hint: | Isolate terms with x to the left hand side.

Add 6 to both sides:

2 x = e^2 + 6

Hint: | Solve for x.

Divide both sides by 2:

Answer: x = e^2/2 + 3