Final answer:
The solution involves expressing the given logarithms with exponents and then changing them to a common base to equate and solve for the value of each logarithm.
Step-by-step explanation:
To solve this mathematical problem, we need to equate the two given logarithmic expressions and find the value for each logarithm. We have the given equations logb3a2 and loga12b8 being equal. Using the properties of logarithms, we can solve for the values of these expressions.
- Express logarithms with exponents: The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. So, we write the given equations as 2*logb3a and 8*loga12b, respectively.
- Change of base: We can change the bases of the logarithms to a common base using the change of base formula: logbx = logkx / logkb. This allows us to compare the two logarithms directly.
- Equate and solve: After changing to a common base, we can set the two expressions equal to each other and solve for the value of the logarithms.
With the steps mentioned above, we find the value of each logarithm, which are equal to one another due to the initial condition given in the problem.
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