What is the answer to log_{4}((2b+4)/(3b-2))=4 ?

The answer to log_{4}((2b+4)/(3b-2))=4 is b= 258/383

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log_{4}((2b+4)/(3b-2))=4

lo g_{4} (\frac{2 b + 4}{3 b - 2}) = 4

b = \frac{258}{383}

Decimal Notation

b = 0.67362 \dots

Solution steps

lo g_{4} (\frac{2 b + 4}{3 b - 2}) = 4

Apply log rules

\frac{2 b + 4}{3 b - 2} = 4^{4}

Multiply both sides by

3 b - 2

\frac{2 b + 4}{3 b - 2} (3 b - 2) = 4^{4} (3 b - 2)

Simplify

2 b + 4 = 256 (3 b - 2)

Solve

2 b + 4 = 256 (3 b - 2) : b = \frac{258}{383}

b = \frac{258}{383}

Verify Solutions:

b = \frac{258}{383}

True

The solution is

b = \frac{258}{383}

x, ln (\frac{x}{y}) = 1

lo g_{55} (x) = 1

lo g_{3} (6 x - 7) = 2

lo g_{4} (3 x + 1) = 3

lo g_{3} (x + 6) + lo g_{3} (x + 4) = 1

What is the answer to log_{4}((2b+4)/(3b-2))=4 ?
The answer to log_{4}((2b+4)/(3b-2))=4 is b= 258/383
Solve for b: log_{4}((2b+4)/(3b-2))=4
The solution is b= 258/383