Question

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

Answer 1

Answer:

$x=\frac{log(2)}{log(10)}$

Step-by-step 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:

$x=\frac{log(2)}{log(10)}$

for y=1

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

$log(1)+x=\frac{log(2)}{log(10)}$

$log(1)=0$

so:

$x=\frac{log(2)}{log(10)}$

Hence:

$x=\frac{log(2)}{log(10)}$