Basic Math Examples

$h = - 64 t^{2 + pt + k}$

Step 1

Rewrite the equation as $- 64 t^{2 + p t + k} = h$ .

$- 64 t^{2 + p t + k} = h$

Step 2

Divide each term in $- 64 t^{2 + p t + k} = h$ by $- 64$ and simplify.

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Step 2.1

Divide each term in $- 64 t^{2 + p t + k} = h$ by $- 64$ .

$\frac{- 64 t^{2 + p t + k}}{- 64} = \frac{h}{- 64}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 64$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 64 t^{2 + p t + k}}{- 64} = \frac{h}{- 64}$

Step 2.2.1.2

Divide $t^{2 + p t + k}$ by $1$ .

$t^{2 + p t + k} = \frac{h}{- 64}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$t^{2 + p t + k} = - \frac{h}{64}$

Step 3

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

$\ln (t^{2 + p t + k}) = \ln (- \frac{h}{64})$

Step 4

Expand $\ln (t^{2 + p t + k})$ by moving $2 + p t + k$ outside the logarithm.

$(2 + p t + k) \ln (t) = \ln (- \frac{h}{64})$

Step 5

Simplify the left side.

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Step 5.1

Apply the distributive property.

$2 \ln (t) + p t \ln (t) + k \ln (t) = \ln (- \frac{h}{64})$

Step 6

Simplify the left side.

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Step 6.1

Move $2 \ln (t)$ .

$p t \ln (t) + k \ln (t) + 2 \ln (t) = \ln (- \frac{h}{64})$

Step 6.2

Reorder $p t \ln (t)$ and $k \ln (t)$ .

$k \ln (t) + p t \ln (t) + 2 \ln (t) = \ln (- \frac{h}{64})$

Step 7

Move all the terms containing a logarithm to the left side of the equation.

$k \ln (t) + p t \ln (t) + 2 \ln (t) - \ln (- \frac{h}{64}) = 0$

Step 8

Expand $\ln (t^{2 + p t + k})$ by moving $2 + p t + k$ outside the logarithm.

$(2 + p t + k) \ln (t) = \ln (- \frac{h}{64})$