Algebra Examples

$\log_{b} (x) = 4 \log_{b} (2) + \log_{b} (3)$

Step 1

Simplify the right side.

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Step 1.1

Simplify $4 \log_{b} (2) + \log_{b} (3)$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Simplify $4 \log_{b} (2)$ by moving $4$ inside the logarithm.

$\log_{b} (x) = \log_{b} (2^{4}) + \log_{b} (3)$

Step 1.1.1.2

Raise $2$ to the power of $4$ .

$\log_{b} (x) = \log_{b} (16) + \log_{b} (3)$

Step 1.1.2

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

$\log_{b} (x) = \log_{b} (16 \cdot 3)$

Step 1.1.3

Multiply $16$ by $3$ .

$\log_{b} (x) = \log_{b} (48)$

Step 2

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$x = 48$