Question

Solve the following x: log base 2(3x-5)=3log2 (3x-5)=3.

Answer 1

Assume that the equation is .

Consider and solve for x.

Apply power property of logarithm : .

Apply One - to - One property of logarithm : If then .

.

Logarithm definition : .

But by the definition of ln or log, (3x - 5) must be positive or 3x - 5 > 0 -----> x > 5/3 = 1.67.Therefore, x must be greater than 5/3 = 1.67.

Here x = 2 is the solution, since x = 2 > 1.67(True).

Here x = 4/3 = 1.3 does not the solution, since x = 1.3 > 1.67(False).

Consider and solve for x.

Exponentiation both sides (with base 2)

Apply inverse property of logarithm : .

.

Consider and solve for x.

Exponentiation both sides (with base 2).

.

The value of .