Question

Solve the following exponential equations.
(10^x)^2 − 3(10^x) + 2 = 0

Answer 1

`x=(log(2))/(log(10))`

Explanation:

Let:

`y=10^(x)`

So, rewritting the equation:

`y^(2) -3y+2=0`

Factoring:

`(y-2)(y-1)=0`

Therefore:

`y=2\hspace{5}or\hspace{5}y=1`

Substitute back for
`y=10^(x)`

for y=2

Taking the logarithm base 10 of both sides:

`x=(log(2))/(log(10))`

for y=1

Taking the logarithm base 10 of both sides and adding 1 to both sides:

`log(1)+x=(log(2))/(log(10))`

`log(1)=0`

so:

`x=(log(2))/(log(10))`

Hence:

`x=(log(2))/(log(10))`