Solve for x in terms of b
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Solve for x in terms of b

[From: ] [author: ] [Date: 12-04-21] [Hit: ]
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Solve for x in terms of b.

log_b (1 - 3x) = 3 + logsub_b (x)

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log_b (1 - 3x) = 3 + log_b (x)

log_b (1 - 3x) - log_b (x) = 3

log_b (1 - 3x)/x = 3 <--- log m - log n = log (m/n)

b^3 = ( 1 - 3x ) / x <--- express in exponential form

b^3 = 1/x - 3 <--- separate into 2 fractions

b^3 + 3 = 1/x <--- isolate the x

1/(b^3 + 3) = x <--- take the reciprocal of both sides

x = 1/(b^3 + 3)

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log_b(1-3x)-log_b(x)=3

log_b((1-3x)/x))=3

(1-3x)/x = b^3

1/x-3 = b^3 for x not equal to zero.

1/x =b^3+3

x= 1/(b^3+3)

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logb (1 - 3x) = 3 + logb (x)
logb (1 - 3x) = logb (b^3) + logb (x)
logb (1 - 3x) = logb (xb^3)
1 - 3x = xb^3
xb^3 + 3x = 1
x(b^3 + 3) = 1
x = 1 / (b^3 + 3)
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