Logarithm Question: Solve 4^(x + 3) = 6^(x - 2)

[KarlyD]

Hey,

Having some issues with this one. Here's my work - if you can let me know what I'm doing wrong, I'd really appreciate it. I've already approached my prof about my problems this question, and he told me to "sit down and figure it out". :shock:

4^(x+3) = 6 ^(x-2)

Step One: log4^(x+3) = log6^(x-2)

Step Two: (x+3)log4 = (x-2)log6

Step Three: xlog4 + 3log4 + 2log6 = xlog6 - 2log6 + 2log6

Step Four: xlog4 + 3log4 + 2 log 6 over log6 = xlog 6 over log 6

Step Five: log6^2 + ?
Having the x in xlog4 + 3log 4 is throwing me off.

 

[stapel]

Get the x-terms together:

. . . . .x log(4) + 3 log(4) = x log(6) - 2 log(6)

. . . . .3 log(4) + 2 log(6) = x log(6) - x log(4)

. . . . .log(64) + log(36) = x [ log(6) - log(4) ]

. . . . .log(64 × 36) = x log(6/4)

And so forth. After simplifying inside the logs, divide through to isolate x.

Eliz.

 

[KarlyD]

Thanks a lot.