The variables x and y satisfy the equation y=A(b^-x), where A and b are constants. The graph of ln y against x is a straight line passing through the points (0, 1.3) and (1.6, 0.9). Find the values of A and b, correct to 2 decimal places.

so this means

and so

Solve: -5=-6+2e^(-2x)

:) 

16^(x+4)=8^(3x-2)

For this example our strategy is to make the bases equal, then we can set the exponents equal:

so x=22/5 

Solve the exponential equation a)(2^x)(2^x)=64

Solve: 3(10000)^n -27 = 299973.

(3(10000)^n -27+27)/3 = (299973+27)/3
10000^n=100000
10^(4n)=10^5
4n=5
n=5/4

Solve: 5^(2x)-3*5^x+2=0

if

then we have
 or 
and therefore
 or 

6^x=13^x/4 find value of x

Multiply bot sides by 4, divide both sides by 6^x to get

taking logs...

Solve for x : 15^(2x)=36

Solve: 3(4^2x)+5(4^x)-2=0

u+2 is extraneous, assuming all solutions are to be real



Taking log base 4 of both sides...

If 8^x=4, solve for x

Solve for x: 9^(7x-9)=5^(9x-9)

Taking ln of both sides leads to:






which is linear and simplifies to...

how would you solve the equation 3^(x-20)=1