## 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 $x^{(log_{10})^2-(log_{10}x^3 +1}\gt 1000$

Summary

Article Name

Logarithm function and properties.

Description

Practice on definition and properties of logarithms.

Author

Mathsdiscussion

Publisher Name

Mathsdiscussion.com