Here are three logarithm problems I have to solve:
1. "Find the exact value of x satisfying the equation 3^x*4^(2x+1) = 6^(x+2)
Give your answer in the form ln a/ln b where a and b are real numbers"
For this one, I have attempted to divide the second term out of the first half and then taken the natural log of that, also I have attempted to consolidate the terms by attempting to get the three terms with the same base, but neither were successful.
2. "Solve 2(5^[x+1]) = 1 + (3/5^x), giving the answer in the form of a+log base 5 b"
For this one, I tried to substitute in 'x' for 5^x, thereby getting 2(x^2)-1 = 3/x and worked it out from there. I am not certain if I did something wrong, and thus did not get the right answer, or if the method is inherently flawed.
3. "Find an expression for the sum of the first 35 terms of the series ln x^2 + ln x^2/y + ln x^2/y^2 + ln x^2/y^3 + ln x^2/y^4. Giving your answer in the form ln x^m/y^n, where m, n are natural numbers."
For this one, I got ln x^2a - ln y^s, a being the number of terms, s being the sum of the numbers between 1-34 (595). Thus, I get 2a ln x - s ln y. So I get 70 ln x - 595 ln y. From this I get ln x^70 / y^595. In this problem, I am looking for confirmation of my answer.
Thank you very much,