What is the answer to log_{b}(2)=2.55 ?

The answer to log_{b}(2)=2.55 is b=2^{20/51}

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log_{b}(2)=2.55

lo g_{b} (2) = 2.55

b = 2^{\frac{20}{51}}

Decimal Notation

b = 1.31235 \dots

Solution steps

lo g_{b} (2) = 2.55

Apply log rules

\frac{1}{lo g _{2} ( b )} = 2.55

Multiply both sides by

lo g_{2} (b)

\frac{1}{lo g _{2} ( b )} lo g_{2} (b) = 2.55 lo g_{2} (b)

Simplify

1 = 2.55 lo g_{2} (b)

Switch sides

2.55 lo g_{2} (b) = 1

Multiply both sides by

100

255 lo g_{2} (b) = 100

Divide both sides by

255

lo g_{2} (b) = \frac{20}{51}

Apply log rules

b = 2^{\frac{20}{51}}

Verify Solutions:

b = 2^{\frac{20}{51}}

True

The solution is

b = 2^{\frac{20}{51}}

lo g_{3} (x + 4) + lo g_{3} (x + 4) = 2

lo g_{2 x} (2 x^{2} + 8 x - 6) = 2

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

lo g_{b} (2) = 2.48

ln (x) = - 2 ln (5)

What is the answer to log_{b}(2)=2.55 ?
The answer to log_{b}(2)=2.55 is b=2^{20/51}
Solve for b: log_{b}(2)=2.55
The solution is b=2^{20/51}