Question

1. x^(1-0.25logx)=10
2. log(9)^-1+xlog(3^5x-7)^1/3=0

Answer 1

show how to solve for x? answers are 100 for question 1 and 2 & -3/5 for question 2

Answer 2

Wow these are quite tricky. I was able to do number 1 so far. I hope I can explain this well.

Answer 3

\[\huge x^{\left(1-\frac{1}{4}\log x\right)}=10\]Take the log (base 10), of both sides, giving you,\[\log\left(\huge x^{\left(1-\frac{1}{4}\log x\right)}\right)=\log_{10}10\]

Answer 4

The right side simplifies very nicely.
The left side we can apply a familiar rule of logs,\[\huge \log(a^b)=b \cdot \log (a)\]Applying this to our problem gives us,\[\huge \left(1-\frac{1}{4}\log x\right) \log x=1\]See how the exponent came down?

Answer 5

Where you at blue? +_+

Answer 6

sorry i was attempting to do it haha no luck

Answer 7

yea i see how it comes down

Answer 8

Distribute logx to each term in the brackets, giving us,\[\huge -\frac{1}{4}\log^2 x+\log x=1\]

Answer 9

We'll move the 1 to the other side, then we'll multiply both sides by -4, giving us,\[\huge \log^2 x-4\log x+4=0\]

Answer 10

It's very important that you don't confuse,\[\huge \log^2 x \quad \text{with} \quad \log x^2\]We CAN NOT bring down the 2 in our problem, using rules of logarithms.

Answer 11

thank you so much i can get the answer now :D

Answer 12

k cool c:

Answer 13

yea *-*

Answer 14

The other one is really hard to read, lemme try to format it, and you can tell me if it's correct or not.

Answer 15

\[\huge \log(9^{-1})+x \log\left[\left(3^{(5x-7)}\right)^{1/3}\right]\]

Answer 16

yes thats it :) its written as a cuberoot in my worksheet though

Answer 17

\[\huge \log(3^{-2})+x \log\left[3^{\frac{1}{3}(5x-7)}\right]=0\]Ok I think we can do something like this, then we'll pull the exponent out again,\[\huge -2\cdot \log(3)+\frac{1}{3}(5x-7)\cdot x \log(3)=0\]

Answer 18

Divide both sides by log(3) giving you,\[\huge -2+\frac{1}{3}(5x-7)\cdot x=0\]

Answer 19

I didn't check this one against the answer you posted earlier, so hopefully I didn't make any mistakes in there :O

Answer 20

Yah I got -3/5. So we're on the right track it seems.

Answer 21

i think i get what you did

Answer 22

Confused about any of that shinanigans there? :O lot of weird stuff.

Answer 23

Thanks a lot you're extremely helpful

Answer 24

no i get it

Answer 25

np c:

Answer 26

thanks so much :)