Logarithm Assignment 1
Question 1
1.
Find x such that $(\cfrac{2}{5})^{\cfrac{6-5x}{2-5x}} \lt \cfrac{25}{4}$
Question 2
2.
Find x such that $\cfrac{2^{x-1} -1 }{2^{x+1} + 1} \lt 2$
Question 3
3.
Find x such that $log_3(1+log_3(2^x – 7)) = 1 $
Question 4
4.
Find x such that $log_5(\cfrac{2+x}{10}) =log_5(\cfrac{2}{x+1})$
Question 5
5.
Find x such that $log_2(4 \times 3^x – 6) – log_2(9^x – 6) = 1$
Question 6
6.
Find x such that $log_2(25^{x+3} – 1) = 2 + log_2(5^{x+3} + 1)$
Question 7
7.
Find x such that $3log_x 4 + 2log_{4x} 4 +3log_{16x} 4 =0$
Question 8
8.
Find x such that $log_x(log_9(3^x-9)) \lt 1$
Question 9
9.
Find x such that $\cfrac{log_2(4x^2-x-1)}{log_2(x^2 +1)}\gt 1$
Question 10
10.
Find x such that $x^{(log_{10})^2-(log_{10}x^3 +1}\gt 1000$