26) $$ -9 \cdot 11^{3 r+6}=-32.3 $$

Question

UpStudy AI · Accepted Answer

Solve the equation $$ -9 \cdot 11^{3r+6}=-32.3 $$.
Solve the equation by following steps:
- step0: Solve for $$r$$:
  $$-9	imes 11^{3r+6}=-32.3$$
- step1: Change the sign:
  $$9	imes 11^{3r+6}=32.3$$
- step2: Divide both sides:
  $$\frac{9	imes 11^{3r+6}}{9}=\frac{32.3}{9}$$
- step3: Divide the numbers:
  $$11^{3r+6}=\frac{323}{90}$$
- step4: Take the logarithm of both sides:
  $$\log_{11}{\left(11^{3r+6}ight)}=\log_{11}{\left(\frac{323}{90}ight)}$$
- step5: Evaluate the logarithm:
  $$3r+6=\log_{11}{\left(\frac{323}{90}ight)}$$
- step6: Move the constant to the right side:
  $$3r=\log_{11}{\left(\frac{323}{90}ight)}-6$$
- step7: Divide both sides:
  $$\frac{3r}{3}=\frac{\log_{11}{\left(\frac{323}{90}ight)}-6}{3}$$
- step8: Divide the numbers:
  $$r=\frac{\log_{11}{\left(\frac{323}{90}ight)}-6}{3}$$
- step9: Simplify:
  $$r=\frac{\log_{11}{\left(323ight)}-\log_{11}{\left(90ight)}-6}{3}$$
The solution to the equation $$ -9 \cdot 11^{3r+6}=-32.3 $$ is $$ r=\frac{\log_{11}{(323)}-\log_{11}{(90)}-6}{3} $$.
$$ r = \frac{\log_{11}(323) - \log_{11}(90) - 6}{3} $$

26) \( -9 \cdot 11^{3 r+6}=-32.3 \)

Solución de tutoría real

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions