What is the answer to log_{a}(4)=1.585 ?

The answer to log_{a}(4)=1.585 is a=4^{200/317}

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log_{a}(4)=1.585

lo g_{a} (4) = 1.585

a = 4^{\frac{200}{317}}

Decimal Notation

a = 2.39799 \dots

Solution steps

lo g_{a} (4) = 1.585

Apply log rules

\frac{1}{lo g _{4} ( a )} = 1.585

Multiply both sides by

lo g_{4} (a)

\frac{1}{lo g _{4} ( a )} lo g_{4} (a) = 1.585 lo g_{4} (a)

Simplify

1 = 1.585 lo g_{4} (a)

Switch sides

1.585 lo g_{4} (a) = 1

Multiply both sides by

1000

1585 lo g_{4} (a) = 1000

Divide both sides by

1585

lo g_{4} (a) = \frac{200}{317}

Apply log rules

a = 4^{\frac{200}{317}}

Verify Solutions:

a = 4^{\frac{200}{317}}

True

The solution is

a = 4^{\frac{200}{317}}

4 = ln (5 x + e) - 1

lo g_{10} (3 x + 2) = lo g_{10} (x - 1)

lo g_{3} (8 x) - 4 lo g_{3} (2) = 0

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

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

What is the answer to log_{a}(4)=1.585 ?
The answer to log_{a}(4)=1.585 is a=4^{200/317}
Solve for a: log_{a}(4)=1.585
The solution is a=4^{200/317}