What is the answer to log_{a}(3)=0.565 ?

The answer to log_{a}(3)=0.565 is a=3*3^{87/113}

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log_{a}(3)=0.565

lo g_{a} (3) = 0.565

a = 3 \cdot 3^{\frac{87}{113}}

Decimal Notation

a = 6.98976 \dots

Solution steps

lo g_{a} (3) = 0.565

Apply log rules

\frac{1}{lo g _{3} ( a )} = 0.565

Multiply both sides by

lo g_{3} (a)

\frac{1}{lo g _{3} ( a )} lo g_{3} (a) = 0.565 lo g_{3} (a)

Simplify

1 = 0.565 lo g_{3} (a)

Switch sides

0.565 lo g_{3} (a) = 1

Multiply both sides by

1000

565 lo g_{3} (a) = 1000

Divide both sides by

565

lo g_{3} (a) = \frac{200}{113}

Apply log rules

a = 3 \cdot 3^{\frac{87}{113}}

Verify Solutions:

a = 3 \cdot 3^{\frac{87}{113}}

True

The solution is

a = 3 \cdot 3^{\frac{87}{113}}

lo g_{10} (\frac{x}{3} + 50) = 2

lo g_{10} (\frac{x}{5}) + 3 = 5.3

ln (1 - x) = \frac{1}{3}

50 = 11.936 ln (x) + 13.954

2 lo g_{8} (x + 5) = 3

What is the answer to log_{a}(3)=0.565 ?
The answer to log_{a}(3)=0.565 is a=3*3^{87/113}
Solve for a: log_{a}(3)=0.565
The solution is a=3*3^{87/113}