Question

If log 8 (3x) +5 = log 8 (26), what is the value of x?

Answer 1

x = 0.0002644

Explanation:

`\log _(8)3x + 5 = \log_(8)26\\`

We want get the logs on the same side

`\log _(8)3x-\log_(8)26=-5\\`

When you subtract logs with the same base, the insides get divided

`\log_(8)(3x)/(26) =-5`

If
`\log_(8)x=2\\x = 8^2\\x = 64`

We have to do the same here

`(3x)/(26) =8^-^5\\(3x)/(26)=(1)/(8^5)\\(3x)/(26)=(1)/(32768)\\\\3x = (26)/(32768)\\x=(26)/(32768*3)\\x=(13)/(49152) = 0.0002644`

Answer 2

x=7

Explanation:

3x+5=26

3x=21

x=7