Exponential Functions

[nycmathguy]

For each function, do the following:

1. Solve for x

2. Graph each function on the same xy-plane

3^(2x) - 5^(x^2) = 100^(x^2 - 4)

5^(x + 5) = 6^(x - 5)

 

[MathLover1]

1.

.........you can solve it only using calculator

x≈1.36521
x≈4.5512×10^-9 which is very close to x=0

2.

5log(6)+ 5log(5) = x* log(6)- x*log(5)
5(log(6)+ log(5)) = x(log(6)- log(5))

x=93.28 approximately

 

[nycmathguy]

1. View attachment 3783 .........you can solve it only using calculator

x≈1.36521
x≈4.5512×10^-9 which is very close to x=0

2.

View attachment 3784

View attachment 3785

View attachment 3786
5log(6)+ 5log(5) = x* log(6)- x*log(5)
5(log(6)+ log(5)) = x(log(6)- log(5))
View attachment 3793

x=93.28 approximately

A nice, detailed reply.