x = 0.0002644
Step-by-step explanation:
[tex]\log _{8}3x + 5 = \log_{8}26\\[/tex]
We want get the logs on the same side
[tex]\log _{8}3x-\log_{8}26=-5\\[/tex]
When you subtract logs with the same base, the insides get divided
[tex]\log_{8}\frac{3x}{26} =-5[/tex]
If [tex]\log_{8}x=2\\x = 8^2\\x = 64[/tex]
We have to do the same here
[tex]\frac{3x}{26} =8^-^5\\\frac{3x}{26}=\frac{1}{8^5}\\\frac{3x}{26}=\frac{1}{32768}\\\\3x = \frac{26}{32768}\\x=\frac{26}{32768*3}\\x=\frac{13}{49152} = 0.0002644[/tex]
