What is the answer to solvefor a,log_{a}(a^3)=x ?

The answer to solvefor a,log_{a}(a^3)=x is No Solution for a\in\mathbb{R}

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solvefor a,log_{a}(a^3)=x

solve for

a, lo g_{a} (a^{3}) = x

No Solution for a \in R

Solution steps

lo g_{a} (a^{3}) = x

Apply log rules

\frac{ln ( a )}{ln ( a )} = \frac{x}{3}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

ln (a) \cdot 3 = ln (a) x

Move

ln (a) x

to the left side

ln (a) \cdot 3 - ln (a) x = 0

Factor

ln (a) \cdot 3 - ln (a) x : ln (a) (3 - x)

ln (a) (3 - x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

ln (a) = 0

Apply log rules

a = 1

Verify Solutions:

a = 1

False

The solution is

No Solution for a \in R

3 = - 2 x

5 (x - 1) = 4 (x - 2)

- 4 s + 2 (4 s + 1) = 125

\frac{55}{75} = \frac{x}{100}

- 2 - 8 x = - 4 x - 2

What is the answer to solvefor a,log_{a}(a^3)=x ?
The answer to solvefor a,log_{a}(a^3)=x is No Solution for a\in\mathbb{R}