Exponential Equations Practice II

1. $-4\cdot 3^{\large{6w}}=-1750$

   What is the solution of the equation?

   Round your answer, if necessary, to the nearest thousandth.

   $w\approx$

2. $5\cdot 2^{\large{-3t}}=45$

   Which of the following is the solution of the equation?

   Choose 1 answer:

   1. $t=-\dfrac{\log_2(9)}{\log(3)}$
   2. $t=-\dfrac{1}3\log_2(9)$
   3. $t=-\dfrac{1}3\log_9(2)$

   4. $t=-\dfrac{\log_9(2)}{\log(3)}$

3. $500\cdot 5^{\large{\frac{y}{3}}}=1$

   What is the solution of the equation?

   Round your answer, if necessary, to the nearest thousandth.
   

   $y\approx$

4. $4\cdot 2^{\large{-\frac {t}{5}}}=288$
   

   Which of the following is the solution of the equation?
   

   Choose 1 answer:

   1. $t=-5\log_{288}(8)$
   2. $t=-5\log_{72}(2)$
   3. $t=-5\log_8(288)$
   4. $t=-5\log_2(72)$

Source: Khan Academy, https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-eq-log/e/solve-exponential-equations-using-logarithms-base-2
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