Solve for y -100*2^(0.5y)=-5

$- 100 \cdot 2^{0.5 y} = - 5$

Divide each term in $(- 100 \cdot 2^{0.5 y}) = - 5$ by $- 100$ and simplify.

Divide each term in $(- 100 \cdot 2^{0.5 y}) = - 5$ by $- 100$ .

$\frac{(- 100 \cdot 2^{0.5 y})}{- 100} = \frac{- 5}{- 100}$

Simplify the left side.

Cancel the common factor of $- 100$ .

Cancel the common factor.

$\frac{- 100 \cdot 2^{0.5 y}}{- 100} = \frac{- 5}{- 100}$

Divide $2^{0.5 y}$ by $1$ .

$2^{0.5 y} = \frac{- 5}{- 100}$

Simplify the right side.

Cancel the common factor of $- 5$ and $- 100$ .

Factor $- 5$ out of $- 5$ .

$2^{0.5 y} = \frac{- 5 (1)}{- 100}$

Cancel the common factors.

Factor $- 5$ out of $- 100$ .

$2^{0.5 y} = \frac{- 5 \cdot 1}{- 5 \cdot 20}$

Cancel the common factor.

$2^{0.5 y} = \frac{- 5 \cdot 1}{- 5 \cdot 20}$

Rewrite the expression.

$2^{0.5 y} = \frac{1}{20}$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (2^{0.5 y}) = \ln (\frac{1}{20})$

Expand the left side.

Expand $\ln (2^{0.5 y})$ by moving $0.5 y$ outside the logarithm.

$0.5 y \ln (2) = \ln (\frac{1}{20})$

Multiply $\ln (2)$ by $0.5$ .

$0.34657359 y = \ln (\frac{1}{20})$

Divide each term in $0.34657359 y = \ln (\frac{1}{20})$ by $0.34657359$ and simplify.

Divide each term in $0.34657359 y = \ln (\frac{1}{20})$ by $0.34657359$ .

$\frac{0.34657359 y}{0.34657359} = \frac{\ln (\frac{1}{20})}{0.34657359}$

Simplify the left side.

Cancel the common factor of $0.34657359$ .

Cancel the common factor.

$\frac{0.34657359 y}{0.34657359} = \frac{\ln (\frac{1}{20})}{0.34657359}$

Divide $y$ by $1$ .

$y = \frac{\ln (\frac{1}{20})}{0.34657359}$

Simplify the right side.

Replace $e$ with an approximation.

$y = \frac{\log_{2.71828182} (\frac{1}{20})}{0.34657359}$

Divide $1$ by $20$ .

$y = \frac{\log_{2.71828182} (0.05)}{0.34657359}$

Log base $2.71828182$ of $0.05$ is approximately $- 2.99573227$ .

$y = \frac{- 2.99573227}{0.34657359}$

Divide $- 2.99573227$ by $0.34657359$ .

$y = - 8.64385618$

Solve for y -100*2^(0.5y)=-5

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