4 Algebra 2 Questions

Question

1. Solve 2^x=32 and rewrite this equation in a logarithmic form.

2. Analyze the characteristics exponential and logarithmic functions. Make sure you talk about domain and range.
3. Demonstrate at least two different ways how to solve the equation 5^(2x+1)=25.
4. Where in the real world might you find an exponential growth or decay application?

Answer 1

2^x = 32

x =5

2^5 = 2(2)(2)(2)(2) = 32

x = log2(32) = 5 = the log of 32 to the base 2

2^x =32 has domain of any real number

the range is any positive real number

logs have the reverse, domain of any positive number and range of any real number Exponential and logs are inverse functions. If (x,y) is a point on the exponential function, then (y,x) is a point on the log function

5^(2x+1) = 25 = 5^2

2x+1 = 2

2x = 1

x = 1/2

5^(2x+1) = 25

2x+1 = log5(25) = 2

2x =2-1=1

x =1/2

Practical application of decay is carbon dating

application of growth is compound interest