Solve for x 10^(-x)=11

$10^{- x} = 11$

Take the base $10$ logarithm of both sides of the equation to remove the variable from the exponent.

$\log (10^{- x}) = \log (11)$

Expand the left side.

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Expand $\log (10^{- x})$ by moving $- x$ outside the logarithm.

$- x \log (10) = \log (11)$

Logarithm base $10$ of $10$ is $1$ .

$- x \cdot 1 = \log (11)$

Multiply $- 1$ by $1$ .

$- x = \log (11)$

Multiply each term in $- x = \log (11)$ by $- 1$

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Multiply each term in $- x = \log (11)$ by $- 1$ .

$(- x) \cdot - 1 = \log (11) \cdot - 1$

Multiply $(- x) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 x = \log (11) \cdot - 1$

Multiply $x$ by $1$ .

$x = \log (11) \cdot - 1$

Simplify $\log (11) \cdot - 1$ .

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Move $- 1$ to the left of $\log (11)$ .

$x = - 1 \cdot \log (11)$

Rewrite $- 1 \log (11)$ as $- \log (11)$ .

$x = - \log (11)$

The result can be shown in multiple forms.

Exact Form:

$x = - \log (11)$

Decimal Form:

$x = - 1.04139268 \dots$

Solve for x 10^(-x)=11

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