Question 250331
Let's take this part by part:
1. Express as a single logarithm and if possible, simplify.
{{{Log_a(x^3) - 2log_a(sqrt(3x))}}}
Step 1 - use the power rule and bring the 2 up to the exponent:
{{{Log_a(x^3) - (log_a(sqrt(3x))^2)}}}
step 2 - rewrite the square root a 1/2 power and cancel with the 2.
{{{Log_a(x^3) - log_a(3x)}}}
step 3 - since the bases are the same and we are subtracting, we can combine and make this division as
{{{Log_a(x^3/3x)}}}
step 4 - we can reduce by x; assuming x is not 0 as
{{{Log_a(x^2/3)}}}
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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.
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3. Express as a sum, difference, and product of logarithms, without using exponents: 
{{{(Log(2x)^(5y^8))}}}/{{{4}}}
step 1 - since 5y^8 is the big exponent, that comes out front using power rule
{{{((5y^8)*log(2x))/4}}}
step 2 - since we are multiplying 2 and x, we can split it using addition as
{{{((5y^8)/4)*(log(2) + log(a))}}}