Solve for x log base 3 of 243=2x+1

$\log_{3} (243) = 2 x + 1$

Step 1

Rewrite the equation as $2 x + 1 = \log_{3} (243)$ .

$2 x + 1 = \log_{3} (243)$

Step 2

Logarithm base $3$ of $243$ is $5$ .

Rewrite as an equation.

$2 x + 1 = \log_{3} (243) = x$

Rewrite $\log_{3} (243) = x$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b$ does not equal $1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$2 x + 1 = 3^{x} = 243$

Create equivalent expressions in the equation that all have equal bases.

$2 x + 1 = 3^{x} = 3^{5}$

Since the bases are the same, the two expressions are only equal if the exponents are also equal.

$2 x + 1 = x = 5$

The variable $x$ is equal to $5$ .

$2 x + 1 = 5$

Step 3

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$2 x = 5 - 1$

Subtract $1$ from $5$ .

$2 x = 4$

Step 4

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$

Solve for x log base 3 of 243=2x+1

Related Questions

Support LCMGCF.com by disabling your adblocker.