More Exponential Equations

Solve 5^(x + 1) + 10^(x - 1) = 15^(2x - 1)

 

Solving Exponential Equations:
Step 1: Express both sides in terms of the same base.
Step 2: Equate the exponents.
Step 3: Solve the resulting equation.
Solve. ...

or
Step 1: Isolate the exponential and then apply the logarithm to both sides.

or
sometimes have to use calculator


5^(x + 1) + 10^(x - 1) = 15^(2x - 1)

5^(x + 1) =5*5^x

10^(x - 1)=(5^x*2^x)/10

15^(2x - 1)=15^(2x)/ 15 =(3^(2x)*5^(2x))/15

5*5^x +(5^x*2^x)/10=(3^(2x)*5^(2x))/15 ...........simplify

2 *45^x = 3 (2^x + 50)..........use calculator and you get

x≈1.14557

 

Beautifully done.