What is the answer to 1/5 log_{x}(16)=-1.6 ?

The answer to 1/5 log_{x}(16)=-1.6 is x= 1/(sqrt(2))

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1/5 log_{x}(16)=-1.6

\frac{1}{5} lo g_{x} (16) = - 1.6

x = \frac{1}{2}

Decimal

x = 0.70710 \dots

Solution steps

\frac{1}{5} lo g_{x} (16) = - 1.6

Multiply both sides by

5

lo g_{x} (16) = - 8

Apply log rules

\frac{1}{lo g _{16} ( x )} = - 8

Multiply both sides by

lo g_{16} (x)

\frac{1}{lo g _{16} ( x )} lo g_{16} (x) = - 8 lo g_{16} (x)

Simplify

1 = - 8 lo g_{16} (x)

Switch sides

- 8 lo g_{16} (x) = 1

Divide both sides by

- 8

lo g_{16} (x) = - \frac{1}{8}

Apply log rules

x = \frac{1}{2}

Verify Solutions:

x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

lo g_{3} (- 9 x) - 10 = - 6

2 ln (8 x - 3) - 3 = 5

2 \cdot lo g_{10} (x - 3) = lo g_{10} (25)

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

lo g_{3} (x) = - \frac{1}{2}

What is the answer to 1/5 log_{x}(16)=-1.6 ?
The answer to 1/5 log_{x}(16)=-1.6 is x= 1/(sqrt(2))
Solve for x: 1/5 log_{x}(16)=-1.6
The solution is x= 1/(sqrt(2))