SOLUTION: 1) Given that base 3 log of x =p find in terms of p in the simplest form : base 3 log of 81x and base 3 log of x^3/9 Hence or otherwise solve base 3 log of (81x)

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Question 350250: 1) Given that base 3 log of x =p find in terms of p in the simplest form :
base 3 log of 81x and base 3 log of x^3/9
Hence or otherwise solve base 3 log of (81x) - base 3 log of (x^3/9) = 7
giving your answer as a surd in the simplest form
I am getting 7/8 as my answer and since this is not a surd,I don't think its the correct solution.

2)Given that 2 base y log x + 2 base x log y =5
show that base y log x= 2 or base y log x=1/2
Hence or otherwise solve : 2 base y log x+ 2 base x log y =5 and xy=27
THANK YOU!
Answer by jsmallt9(3759) (Show Source):
You can put this solution on YOUR website!

Using a property of logarithms, , we can separate the 81 and the x:

Since the first log is 4. The second is p. So

Using a property of logarithms, , we can separate the numerator and the denominator:

Since the second log is 2:

Using yet another property of logarithms, , we can move the exponent in the argument out in front:

The remaining log is p. So:

Now the equation.

Substituting the expressions we found earlier for these two logarithms we have:

(Note the use of parentheses. It is an extremely good habit to use parentheses when making substitutions like this. In this case, it helps us know that the entire expression 3p-2 should be subtracted!)
Simplifying we get:

Solving for p:

And the last part is to replace p and solve for x:

Rewriting this in exponential form we get:

The negative in the exponent tells us reciprocal. The 1/2 tells us square root:

Rationalizing the denominator:

SOLUTION: 1) Given that base 3 log of x =p find in terms of p in the simplest form : base 3 log of 81x and base 3 log of x^3/9 Hence or otherwise solve base 3 log of (81x) - base 3 log