Solve in terms of b: \log_b (1 - 3x) = 3

estrigaslju 2022-04-22 Answered
Solve in terms of b:
logb(13x)=3+logbx
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Answers (1)

Gianna Travis
Answered 2022-04-23 Author has 11 answers
Remember, any log to the base b, such as logb(y), is in its heart an exponent. Let us start, then, from your expression
logb(13xx)=3.
Raise b to the powers we see on each side. We get
blogb(13xx)=b3.
The left-hand side simplifies greatly. We get
13xx=b3.
The rest is elementary algebra. The above equation is (for x0) equivalent to
13x=b3x,
which is an easily solved linear equation.
Comment: There was no need to do the preliminary manipulation. We are told that
logb(13x)=3+logbx.
Raise b to the power on the left-hand side, the right-hand side. We obtain
blogb(13x)=b3+logbx.
By the "laws of logarithms" this yields
13x=b3x.
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