Solve for $$ x $$ : $$ \frac{9}{5} \log _{5} x=2 $$ $$ x=\square $$ You may enter the exact value or round to 4 significant decimal places.

Question

UpStudy AI · Accepted Answer

Solve the equation $$ \frac{9}{5} \log _{5} x=2 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{9}{5}\log_{5}{\left(xight)}=2$$
- step1: Find the domain:
  $$\frac{9}{5}\log_{5}{\left(xight)}=2,x>0$$
- step2: Multiply by the reciprocal:
  $$\frac{9}{5}\log_{5}{\left(xight)}	imes \frac{5}{9}=2	imes \frac{5}{9}$$
- step3: Multiply:
  $$\log_{5}{\left(xight)}=\frac{10}{9}$$
- step4: Convert the logarithm into exponential form:
  $$x=5^{\frac{10}{9}}$$
- step5: Transform the expression:
  $$x=5\sqrt[9]{5}$$
- step6: Check if the solution is in the defined range:
  $$x=5\sqrt[9]{5},x>0$$
- step7: Find the intersection:
  $$x=5\sqrt[9]{5}$$
The solution to the equation $$ \frac{9}{5} \log _{5} x=2 $$ is $$ x=5\sqrt[9]{5} $$ or approximately $$ x \approx 5.979066 $$.
$$ x = 5\sqrt[9]{5} $$ or approximately $$ x \approx 5.9791 $$.

Solve for \( x \) : \( \frac{9}{5} \log _{5} x=2 \) \( x=\square \) You may enter the exact value or round to 4 significant decimal places.

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Algebra Questions