SOLUTION: What's the value of N? log{{{7}}}n = 2/3log{{{7}}}8 I have no idea what I'm even supposed to do first. By the way 2/3 is the fraction two thirds. I'd really appreciate it if you wa

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What's the value of N? log₇n = 2/3log₇8 I have no idea what I'm even supposed
to do first. By the way 2/3 is the fraction two thirds. I'd really appreciate
it if you walk me through it. THANKS
`
log<sub>7</sub>n = 2/3·log<sub>7</sub>8
`
Use the rule N·log_BU = log_BU^N on the right side
`
log<sub>7</sub>n = log<sub>7</sub>8<sup>2/3</sup>
`
Now write 8 as 2³
`
log<sub>7</sub>n = log<sub>7</sub>(2<sup>3</sup>)<sup>2/3</sup>
`
Now simplify (2³)^2/3 to 2^3·2/3 = 2¹ = 2
`
log<sub>7</sub>n = log<sub>7</sub>2
`
Now raise both sides to the 7 power, which amounts to dropping the logs
`
n = 2
`
Edwin
AnlytcPhil@aol.com