What is the answer to 18=10log_{10}((200)/x) ?

The answer to 18=10log_{10}((200)/x) is x=10^{1/5}*2

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18=10log_{10}((200)/x)

18 = 10 lo g_{10} (\frac{200}{x})

x = 1 0^{\frac{1}{5}} \cdot 2

Decimal Notation

x = 3.16978 \dots

Solution steps

18 = 10 lo g_{10} (\frac{200}{x})

Switch sides

10 lo g_{10} (\frac{200}{x}) = 18

Divide both sides by

10

lo g_{10} (\frac{200}{x}) = \frac{9}{5}

Apply log rules

\frac{200}{x} = 1 0^{\frac{9}{5}}

Multiply both sides by

x

\frac{200}{x} x = 1 0^{\frac{9}{5}} x

Simplify

1 0^{\frac{9}{5}} x : 1 0^{1 + \frac{4}{5}} x

200 = 1 0^{1 + \frac{4}{5}} x

Solve

200 = 1 0^{1 + \frac{4}{5}} x : x = 1 0^{\frac{1}{5}} \cdot 2

x = 1 0^{\frac{1}{5}} \cdot 2

Verify Solutions:

x = 1 0^{\frac{1}{5}} \cdot 2

True

The solution is

x = 1 0^{\frac{1}{5}} \cdot 2

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

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

lo g_{3} (- 7 x + 1) - 7 = - 4

lo g_{3} (32) = 5 lo g_{3} (x)

6 lo g_{49} (r) = 3

What is the answer to 18=10log_{10}((200)/x) ?
The answer to 18=10log_{10}((200)/x) is x=10^{1/5}*2
Solve for x: 18=10log_{10}((200)/x)
The solution is x=10^{1/5}*2