Properties of Logs
Rewrite as a single logarithm
2\log_4x-6\log_4y
\log_4\frac{x^2}{y^6}
What's the transformation?
\log(x)+10
Vertical translation up 10
Solve for x
\log_2(x-3)=5
35
Solve the inequality
\log_5(x+8)-6<-4
(−8,17)
Rewrite as a single logarithm
6\lnx+\frac1{2}\lny
\lnx^6\sqrty
What's the transformation?
\log_5(5x-5)
Vertical translation up 1. Horizontal translation right 1.
Solve for x
2(3^{4x})=40
\approx0.682
Solve the inequality
\log_3(2x-3)>=3
[15,\infty)
Rewrite as a single logarithm
\frac1{3}(\logx+2\logy)
\log\root[3]{xy^2}
What's the transformation?
\log_3(9x)
Vertical translation up 2
Solve for x
\frac1{2}e^{x-4}=14
\approx0.7332
Solve the inequality
\log_2(x-3)-5>=-1
(19,\infty)
Write in simplest form
\log(10x-30)
1+\log(x-3)
What's the transformation?
\log_2(16x)
Vertical translation up 4
Solve for x
\log(x-3)+\log(x-4)=\log(7-x)
5
Solve the inequality
\log_2(x-7)<3
(7,15)
Write in simplest form
\log_6\sqrt{x^3y^5}
\frac1{2}(3\log_6x+5\log_6y)
What's the transformation?
\log_2(32-8x)
Vertical translation up 3. Horizontal reflection. Horizontal shift right 4.
Solve for x
15+\log_2(2x)=20
16
Solve the inequality
2\cdot3^{x-2}+6<=24
(\infty,4]