1) What is the exponential form of the logarithmic equation? 4=log_{0.8 }04096

2) Solve the logarithmic equation. y=log_{5}125

3) What are the x and y intercepts of the equation? y=log(3x+4)+2 Round the answers to the nearest hundredth.

Thank you :)

Johnnyboy
Nov 20, 2018

#1**+2 **

1) Exponential form is :

0.8^4 = 0.4096

2) This says that 5^y = 125

Note 125 = 5^3

So.... 5^y = 5^3 implies that y = 3

3) y = log (3x + 4) +2

To find the y intercept, set x = 0 and we have

y = log (3(0) + 4) + 2

y = log(4) + 2 ≈ 2.60

To find the x intercept, set y = 0 and we have

0 =log (3x + 4) + 2 subtract 2 from both sides

-2 = log (3x + 4)

In exponential form, we have

10^(-2) = 3x + 4 subtract 4 from both sides

10^(-2) - 4 = 3x divide both sides by 3

[ 10^(-2) - 4 ] / 3 = x = -1.33

CPhill
Nov 20, 2018