Basic Math Examples

$D = 10 \log (5.6 \cdot 10^{15})$

Step 1

Simplify $10 \log (5.6 \cdot 10^{15})$ by moving $10$ inside the logarithm.

$D = \log ({(5.6 \cdot 10^{15})}^{10})$

Step 2

Apply the product rule to $5.6 \cdot 10^{15}$ .

$D = \log ({5.6}^{10} \cdot {(10^{15})}^{10})$

Step 3

Raise $5.6$ to the power of $10$ .

$D = \log (30330548.9096114 \cdot {(10^{15})}^{10})$

Step 4

Multiply the exponents in ${(10^{15})}^{10}$ .

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Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$D = \log (30330548.9096114 \cdot 10^{15 \cdot 10})$

Step 4.2

Multiply $15$ by $10$ .

$D = \log (30330548.9096114 \cdot 10^{150})$

Step 5

Move the decimal point in $30330548.9096114$ to the left by $7$ places and increase the power of $10^{150}$ by $7$ .

$D = \log (3.03305489 \cdot 10^{157})$

Step 6

The result can be shown in multiple forms.

Scientific Notation:

$D = \log (3.03305489 \cdot 10^{157})$

Expanded Form:

$D = 157.48188027$