What is the answer to log_{b}(5)=1.4 ?

The answer to log_{b}(5)=1.4 is b=5^{5/7}

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log_{b}(5)=1.4

lo g_{b} (5) = 1.4

b = 5^{\frac{5}{7}}

Decimal Notation

b = 3.15692 \dots

Solution steps

lo g_{b} (5) = 1.4

Apply log rules

\frac{1}{lo g _{5} ( b )} = 1.4

Multiply both sides by

lo g_{5} (b)

\frac{1}{lo g _{5} ( b )} lo g_{5} (b) = 1.4 lo g_{5} (b)

Simplify

1 = 1.4 lo g_{5} (b)

Switch sides

1.4 lo g_{5} (b) = 1

Multiply both sides by

10

14 lo g_{5} (b) = 10

Divide both sides by

14

lo g_{5} (b) = \frac{5}{7}

Apply log rules

b = 5^{\frac{5}{7}}

Verify Solutions:

b = 5^{\frac{5}{7}}

True

The solution is

b = 5^{\frac{5}{7}}

lo g_{3} (x - 19) = 4

4 ln (3 x) = - 8

lo g_{10} (x) 49 = 2

- 3 = 20 lo g_{10} (2 x)

5 ln (4 x + 3) - 1 = 19

What is the answer to log_{b}(5)=1.4 ?
The answer to log_{b}(5)=1.4 is b=5^{5/7}
Solve for b: log_{b}(5)=1.4
The solution is b=5^{5/7}