SOLUTION: Hello, How would I do the following: 1. Express as a single logarithm and if possible, simplify. {{{Loga x^3-2 loga sqrt^3 x}}} 2. Choose the expression or equation

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Question 250331: Hello,
How would I do the following:
1. Express as a single logarithm and if possible, simplify.

2. Choose the expression or equation that is equivalent to the one given
Logx 29=5
a. 29^x=5
b. X^29=5
c. 5^x=29
d. X^5=29
My answer is "d" is that right?
3. Express as a sum, difference, and product of logarithms, without using exponents.
I am really lost, this is part of a test, and I can to figure them out, can you please help me.

Answer by drk(1908) (Show Source):
You can put this solution on YOUR website!
Let's take this part by part:
1. Express as a single logarithm and if possible, simplify.

Step 1 - use the power rule and bring the 2 up to the exponent:

step 2 - rewrite the square root a 1/2 power and cancel with the 2.

step 3 - since the bases are the same and we are subtracting, we can combine and make this division as

step 4 - we can reduce by x; assuming x is not 0 as

--
2. Choose the expression or equation that is equivalent to the one given
Log_x(29) = 5
a. 29^x=5
b. X^29=5
c. 5^x=29
d. X^5=29
My answer is "d" is that right?
[D] is correct.
--
3. Express as a sum, difference, and product of logarithms, without using exponents:
/
step 1 - since 5y^8 is the big exponent, that comes out front using power rule

step 2 - since we are multiplying 2 and x, we can split it using addition as