Solve (81 * 3 ^ (2x))/(3 ^ 3) = 1 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{81\times3^{2x}}{3^{3}}=1$$

Solve for x

$x=-\frac{1}{2}=-0.5$

Steps Using Definition of Logarithm

Calculate $3$ to the power of $3$ and get $27$.

$$\frac{81\times 3^{2x}}{27}=1$$

Divide $81\times 3^{2x}$ by $27$ to get $3\times 3^{2x}$.

$$3\times 3^{2x}=1$$

Divide both sides by $3$.

$$3^{2x}=\frac{1}{3}$$

Take the logarithm of both sides of the equation.

$$\log(3^{2x})=\log(\frac{1}{3})$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$2x\log(3)=\log(\frac{1}{3})$$

Divide both sides by $\log(3)$.

$$2x=\frac{\log(\frac{1}{3})}{\log(3)}$$

By the change-of-base formula $\frac{\log(a)}{\log(b)}=\log_{b}\left(a\right)$.

$$2x=\log_{3}\left(\frac{1}{3}\right)$$

Divide both sides by $2$.

$$x=-\frac{1}{2}$$

Solve for x (complex solution)

$x=\frac{\pi n_{1}i}{\ln(3)}-\frac{1}{2}$
$n_{1}\in \mathrm{Z}$