Using knowledge of logarithmic functions and logarithmic equations, determine the restriction(s) on the variable x in the following equation.

Question

Equation: log(2x-5) + log(x-3) = 1

Once stated and explained the restriction(s), include a solution to the equation in your response.

Answer 1

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Answer 2

2x - 5 > 0 and x - 3 > 0

x > 2.5 and x > 3.

So, x > 3 (1)

log[(2x - 5)(x - 3)] = 1;

So, 2x² - 11x + 15 = 10; 2x² - 11x + 5 = 0; (x - 5)(2x - 1) = 0; x = 5 or x = 1/2

From (1) we have to reject x = 1/2.

Answer: x = 5

Answer 3

2x-5> 0

2x>5

x> 5/2

x-3 > 0

x > 3

x = about 4

if you interpret log as natural log. While ln is used for natural log, log itself can be used that way too. Although in early math courses log tends to be a common log with base 10

ln(2(4)-5) = ln3 = a little less than 1.1

ln(4-3) = ln1 = 0

1.1 + 0 is close to 1

If you intended to use log as base 10

then log(2(5)-5) = log5 = about 0.7

and log(5-3) = log2 = about 0.3

.7+.3 = 1

for natural log, with base e, the solution to the equation is about 4

for common log, with base 10, the solution is 5