Logarithm Function: Properties and Solutions [Attached Image]

[Victim]

Homework Statement

I have attached image of question.[/B]

Homework Equations

all the properties of log
a^(logₘn)=n^(logₘa)[/B]

The Attempt at a Solution

in the attached image

[/B]

 

[George Jones]

$\log _3 \left( a^{\log _3 7} \right)$ is of the form $\log _3 \left( a^y \right)$, Can you simplify this further?

 

[Victim]

$\log _3 \left( a^{\log _3 7} \right)$ is of the form $\log _3 \left( a^y \right)$, Can you simplify this further?

and then

 

[jedishrfu]

and then

You tell us, George gave you a hint.

 

[Victim]

You tell us, George gave you a hint.

OK by this method I got a=20 b=38 c=√(11)-25
Then they are in power of log₃7,log₇11 and log₁₁25.How to solve these powers

 

[SammyS]

OK by this method I got a=20 b=38 c=√(11)-25
Then they are in power of log₃7,log₇11 and log₁₁25.How to solve these powers

The problem states that a, b, and c are positive. The value you give for c, $\ \sqrt{11\,}-25\,,\$ is negative.

Moreover, as it turns out, a, b, and c are all irrational. Fortunately, you do not need to solve for any of them to solve this problem.

Here is a hint that's different than the one given by George Jones.

Notice that $\displaystyle \ X^{Y^ 2}=X^{Y\cdot Y}=\left(X^Y\right)^Y \$​

.