Suppose that $3^a = 2$ and $3^b = 5$. If \\[3^x = 150,\\]then write an expression for $x$ in terms of $a$ and $b$.
Answer
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Use logarithms to solve for a.
Similarly, for b and x.
Factorize 150:
150 = 2 • 3 • 5²
Then we can expand log₃(150) using the product-to-sum and exponent property,