Basic Math Examples

$850 = 1960 \cdot 2^{b}$

Step 1

Rewrite the equation as $1960 \cdot 2^{b} = 850$ .

$1960 \cdot 2^{b} = 850$

Step 2

Divide each term in $1960 \cdot 2^{b} = 850$ by $1960$ and simplify.

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Step 2.1

Divide each term in $1960 \cdot 2^{b} = 850$ by $1960$ .

$\frac{1960 \cdot 2^{b}}{1960} = \frac{850}{1960}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $1960$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{1960 \cdot 2^{b}}{1960} = \frac{850}{1960}$

Step 2.2.1.2

Divide $2^{b}$ by $1$ .

$2^{b} = \frac{850}{1960}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $850$ and $1960$ .

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Step 2.3.1.1

Factor $10$ out of $850$ .

$2^{b} = \frac{10 (85)}{1960}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $10$ out of $1960$ .

$2^{b} = \frac{10 \cdot 85}{10 \cdot 196}$

Step 2.3.1.2.2

Cancel the common factor.

$2^{b} = \frac{10 \cdot 85}{10 \cdot 196}$

Step 2.3.1.2.3

Rewrite the expression.

$2^{b} = \frac{85}{196}$

Step 3

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

$\ln (2^{b}) = \ln (\frac{85}{196})$

Step 4

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

$b \ln (2) = \ln (\frac{85}{196})$

Step 5

Divide each term in $b \ln (2) = \ln (\frac{85}{196})$ by $\ln (2)$ and simplify.

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Step 5.1

Divide each term in $b \ln (2) = \ln (\frac{85}{196})$ by $\ln (2)$ .

$\frac{b \ln (2)}{\ln (2)} = \frac{\ln (\frac{85}{196})}{\ln (2)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (2)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{b \ln (2)}{\ln (2)} = \frac{\ln (\frac{85}{196})}{\ln (2)}$

Step 5.2.1.2

Divide $b$ by $1$ .

$b = \frac{\ln (\frac{85}{196})}{\ln (2)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$b = \frac{\ln (\frac{85}{196})}{\ln (2)}$

Decimal Form:

$b = - 1.20531890 \dots$