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To solve the equation
, we can utilize the property of logarithms that states if the bases are the same, the exponents must also be equal. Thus, we can simplify the equation to:
Now, to remove the logarithm, we rewrite it in exponential form:
Calculating
gives us 16. Hence we have:
Subtracting 8 from both sides yields:
Now, let’s consider some tips. First, double-check your logarithmic properties to avoid misapplication, particularly with different bases. Common mistakes often arise in misunderstanding exponential forms; practice makes perfect! Also, remember that the logarithm of zero or a negative number is undefined, so ensure your solutions are valid within the domain of the logarithm involved. Happy solving!