What is the answer to log_{b}(2)=2.48 ?

The answer to log_{b}(2)=2.48 is b=2^{25/62}

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log_{b}(2)=2.48

lo g_{b} (2) = 2.48

b = 2^{\frac{25}{62}}

Decimal Notation

b = 1.32246 \dots

Solution steps

lo g_{b} (2) = 2.48

Apply log rules

\frac{1}{lo g _{2} ( b )} = 2.48

Multiply both sides by

lo g_{2} (b)

\frac{1}{lo g _{2} ( b )} lo g_{2} (b) = 2.48 lo g_{2} (b)

Simplify

1 = 2.48 lo g_{2} (b)

Switch sides

2.48 lo g_{2} (b) = 1

Multiply both sides by

100

248 lo g_{2} (b) = 100

Divide both sides by

248

lo g_{2} (b) = \frac{25}{62}

Apply log rules

b = 2^{\frac{25}{62}}

Verify Solutions:

b = 2^{\frac{25}{62}}

True

The solution is

b = 2^{\frac{25}{62}}

ln (x) = - 2 ln (5)

7.25 = - 2 lo g_{10} (2 x + 5)

lo g_{10} (3 x - 4) = 2

lo g_{10} (3 x - 4) = 3

ln (2 m + 3) = 8

What is the answer to log_{b}(2)=2.48 ?
The answer to log_{b}(2)=2.48 is b=2^{25/62}
Solve for b: log_{b}(2)=2.48
The solution is b=2^{25/62}