Final answer:
To calculate the value of log base 2 of 3 times log base 3 of 4, we would typically use log properties and a calculator, as there is no straightforward simplification available because the bases are prime relative to each other. The final result is the product of the individual log values calculated using the change of base formula.
Step-by-step explanation:
To solve the mathematical problem completely, we need to calculate the value of log base 2 of 3 times log base 3 of 4. Using the property of logarithms that states the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number, the expression can be simplified. First, let's address log base 2 of 3:
log23 = x => 2x = 3
Now, let's consider log base 3 of 4:
log34 = y => 3y = 4
Our expression is then:
x * y = (log23) * (log34)
Since we do not have the exact values of x and y, we can either leave the expression as it is, or for an exact numerical result, we would typically use a calculator. However, if you're interested in the product of these two logs, it can be found using the change of base formula.
Notice though, this problem does not have a straightforward simplification without the use of a calculator, because the bases are prime relative to each other and their exponents do not suggest a conversion that simplifies the calculation.
Therefore, the best approach to solve this would be to use a calculator to find the decimal values of both logs and then multiply them together for the final answer.