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In summary, the conversation revolves around simplifying the expression ##\log _3 \left( a^{\log _3 7} \right)##, with the hint given to use the property ##a^{(log_m n)}=n^{(log_m a)}##. The attempt at a solution involves solving for a, b, and c with the values of 20, 38, and √(11)-25 respectively, but it is stated that they are not necessary to solve the problem. A different hint is given to help with the simplification process.

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and thenGeorge Jones said:

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You tell us, George gave you a hint.Victim said:and then

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OK by this method I got a=20 b=38 c=√(11)-25jedishrfu said:You tell us, George gave you a hint.

Then they are in power of log₃7,log₇11 and log₁₁25.How to solve these powers

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

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 \ ##

.A logarithm function is the inverse of an exponential function. It helps us solve for the exponent in an exponential equation. In other words, it tells us what power we need to raise a certain base to in order to get a given number.

There are several properties of logarithm functions, including the product rule, quotient rule, power rule, and change of base rule. These properties allow us to manipulate logarithmic expressions and solve for unknown variables.

To graph a logarithm function, you first need to determine the vertical and horizontal asymptotes. Then, you can plot points by choosing a base value, plugging it into the logarithmic equation, and solving for the corresponding y-value. Finally, you can connect the points to create a curve.

The domain of a logarithm function is all positive real numbers, since we cannot take the logarithm of a negative number. The range is all real numbers, since the output of a logarithm function can be any real number depending on the input.

Logarithm functions are used in a variety of fields, including finance, biology, and physics. In finance, they can be used to calculate compound interest. In biology, they can be used to measure the pH scale. In physics, they can be used to calculate the intensity of sound or earthquakes.

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