Log[f(x)] - Math Central

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Question from sourabh, a student:

What is the number of solutions of the equation
9 x 2 - 18 x + 5 = 0 for x, such that the expression
log10[(x+1)(x+2)] exists?

Sourabh,

I think your equation is

9x² - 18x + 5 = 0.

The function on the left of the equal sign factors, so factor it and hence solve for x.

The expression log₁₀[f(x)] exists for all values of x for which f(x) > 0. Substitute the two solutions you found to 9x² - 18x + 5 = 0 into f(x) = (x + 1)(x + 2) to see if this condition is met.

Harley

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