How to solve (3)^(a)=10

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (3)^(a)=10 | Equatix

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$${ 3 }^{ a } =10$$

$a=\log_{3}\left(10\right)\approx 2.095903274$

Use the rules of exponents and logarithms to solve the equation.

$$3^{a}=10$$

Take the logarithm of both sides of the equation.

$$\log(3^{a})=\log(10)$$

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

$$a\log(3)=\log(10)$$

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

$$a=\frac{\log(10)}{\log(3)}$$

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

$$a=\log_{3}\left(10\right)$$

$a=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(10\right)$
$n_{1}\in \mathrm{Z}$