Precalculus Examples

$\log (a) + \log (1 - 2 \log (b))$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (a (1 - 2 \log (b)))$

Step 2

Simplify $- 2 \log (b)$ by moving $2$ inside the logarithm.

$\log (a (1 - \log (b^{2})))$

Step 3

Apply the distributive property.

$\log (a \cdot 1 + a (- \log (b^{2})))$

Step 4

Simplify the expression.

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Step 4.1

Multiply $a$ by $1$ .

$\log (a + a (- \log (b^{2})))$

Step 4.2

Rewrite using the commutative property of multiplication.

$\log (a - a \log (b^{2}))$