(1/3)^x=18 can you compute this

Question

asked Jun 7, 2023 50.9k views

1 Answer

Criticalfix · Answer 1 · 2023-06-13T16:54:56+0000

We have the following equation,

By taking logarithm base 3 to both sides, we have

$\log _3((1)/(3))^x=\log _318$

By the powers rule for logarithms, we get

$x\cdot\log _3((1)/(3))^{}=\log _318$

Now, by the quotient rule, we have that

$\begin{gathered} \log _3((1)/(3))=\log _3(1)-\log _3(3) \\ \log _3((1)/(3))=-\log _3(3) \end{gathered}$

because base 3 logarithm of 1 is zero. Then, we have

$-x\cdot\log _3(3)^{}=\log _318$

But

$\log _3(3)=1$

then, we obtain

$-x=\log _318$

By multiplying both sides by -1, we have

$x=-\log _318$

Finally, since

$\log _318=2.6309$

The answer is x= - 2.6309