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10 cards from this deck
Take logs of both sides of the equation.
Use the rule: log(ab)=b⋅log(a)\log(a^b) = b \cdot \log(a)log(ab)=b⋅log(a).
x=log(2.8)/log(5)≈0.640x = \log(2.8) / \log(5) \approx 0.640x=log(2.8)/log(5)≈0.640 (to 3sf).
You can use either log or ln to solve.
x=log2(7.2)−3≈−1.17x = \log_2(7.2) - 3 \approx -1.17x=log2(7.2)−3≈−1.17 (to 2 decimal places).
Expand to (x+3)log(2)(x + 3) \log(2)(x+3)log(2).
Use product, quotient, and power rules for simplification.
x=(2log(3)+4log(5)−3log(2))/(log(2)+log(5))x = (2\log(3) + 4\log(5) - 3\log(2)) / (\log(2) + \log(5))x=(2log(3)+4log(5)−3log(2))/(log(2)+log(5)).
It equals c⋅loga(b)c \cdot \log_a(b)c⋅loga(b).
Combine: log(x3)=4\log(x^3) = 4log(x3)=4, x3=104x^3 = 10^4x3=104, x=104/3x = 10^{4/3}x=104/3.
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