Probs w/ logs: (1/4)^{log_4(1/3)}, log_{0,2}(0,3) - log_{0,2}(0,5) - log_{0,2}(15)

[Alex7894]

a) (1/4)^{log₄ 1/3 =}
b) log_0,2 0,3 - log_0,2 0,5 - log_0,2 15 =

 

[Deleted member 4993]

a) (1/4)^{log₄ 1/3 =}
b) log_0,2 0,3 - log_0,2 0,5 - log_0,2 15 =

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

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[Alex7894]

Re

Realy sorry :cc.
Well I was able to do that a). And i have problem at this moment and have no idea what power will be there:

 

[mmm4444bot]

… I was able to do that a) …

Good. I got 3.

… have no idea what power will be there [for (2/10)^x=4]

In your work, you wrote 15 as 15/100. But you did not type 0,15 in your first post:

log_0,2 0,3 - log_0,2 0,5 - log_0,215 =

Were we to use 15 as an Integer, we would eventually get:

(1/5)^x = 1/25

---

If that is actually -log_0,2 0,15 then you could simplify part (b) to:

-2 ln(2) / ln(5)

by first rewriting 0,15 as the product (0,3)(0,5) and applying the Product Property of Logarithms.

I cannot read part (c).