# Solving Logarithmic Equations

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A) Solve the equation:

log3 (2 - 3x) = log9 (6x2 - 19x + 2)

b) Prove that if a^x = b^y = (ab)^xy, then:

x + y = 1.

See the attached file.

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#### Solution Preview

Please see the attached file for the complete solution.

a) Solve the equation:

log3 (2 - 3x) = log9 (6x2 - 19x + 2)

Solution:

We know that logxy = log y / log x [Base rule]

Then:

log3(2 - 3x) = log9(6x^2 - 19x +2)

log(2 - 3x) / log 3 = log(6x^2 - 19x +2) / log ...

#### Solution Summary

A logarithmic equation is solved in the solution.

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