0. Functions

Explain why b^x = e^xlnb.

In Exercises 79–84, solve for y.

79. 3^y = 2^(y+1)

Solving equations Solve each equation.

ln 3x + ln (x + 2) = 0

In Exercises 1–4, solve for t.

1. c. e^((ln 0.2)t) = 0.4

Solve the exponential equation.

$2\(\cdot\)10^{3x}=5000$

Solve the exponential equation.

$4^{x+7}=16$

Solving equations Solve the following equations.

ln x= -1

Solving equations Solve the following equations.

7ˣ = 21

Finding all inverses Find all the inverses associated with the following functions, and state their domains.

ƒ(x) = x² -2x + 6

Solve the logarithmic equation.

$\(\log\)_3\(\left\)(3x+9\(\right\))=\(\log\)_35+\(\log\)_312$

Solve the exponential equation.

$e^{2x+5}=8$

In Exercises 79–84, solve for y.

83. ln(y-1) = x + ln(y)