SOLUTION: 1.) log[10](a)+log[10](a+21)=2 2.) log[6](a^2+2)+log[6](2)=2

Question 295377: 1.)
log[10](a)+log[10](a+21)=2
2.)
log[6](a^2+2)+log[6](2)=2
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
1) Solve for a:
Apply the product rule for logarithms:
Simplify the argument on the right side.
Rewrite this in exponential form.
Rearrange into the standard quadratic equation form.
Solve by factoring.
Apply the zero product rule.
or so then...
or Discard the negative solution*.

Check: Substitute a = 4.
=
------------------------------------
2) Solve for a.
Apply the product rule.
Rewrite this in exponential form.
Subtract 4 from both sides.
Divide both sides by 2.
Take the square root of both sides.
or Discard the negative solution*.

*The logarithm of a negative quantity yields a complex number.

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