SOLUTION: i dont know how to solve (3^5x)(9^x^2)=27

Question 70853: i dont know how to solve
(3^5x)(9^x^2)=27
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!

.
Interesting problem.
.
First recognize that can be written as . By the rules of
exponents this can be expanded to and this multiplication can be
done by adding the exponents to get . We can now replace
by . So let's do that very thing. When the substitution is done, the
problem becomes:
.

.
Since these two terms have the common base of 3, the multiplication can be done by adding
the exponents to get:
.

.
Now let's take the log of both sides, and the equation becomes:
.

.
On the left side you can take the exponent away and make it the multiplier of the log term:
.

.
But on the right side the 27 can be replaced by and the equation becomes:
.

.
And now on the right side we can take the exponent out and use it as the multiplier of
the log to make the equation:
.

.
Note that the log(3) is a factor on both sides. If we divide both sides by log(3)
it cancels out and we are left with the "nice" equation:
.

.
Subtract 3 from both sides:
.

.
The left side factors to give:
.

.
Note that if either of the two factors equals 0, the equation will be true. So we can
find the values of x by setting the factors equal to zero.
.

.
Add 1 to both sides and then divide by 2 to find that is a solution.
.
Now set the other factor equal to zero.
.

.
Subtract 3 from both sides and you have:
.
So 1/2 and -3 are the two values of x. If you plug them, one at a time, into the equation
you were given as the problem and work out the resulting equation using a calculator,
you will find that they both work.
.
Like I said at the start, "Interesting problem." Good practice too. I hope you can work
your way through all the steps.
RELATED QUESTIONS
(5X/2) - 1 = (x/3) +12 Cant solve the inequalities because I dont know how to get rid of (answered by josgarithmetic)

(2^1/3 x 3^1/3)^3 i dont know how to solve this can you please... (answered by stanbon)

How do i solve -2lnx+x^2+5. I dont know how to do... (answered by Alan3354)

How do i solve, I know the answer is 8 but i dont know how to get it. 1/2+2/x=3/4 (answered by stanbon)

This is the equation which i have and I dont know how to solve it:... (answered by jsmallt9)

-2+x= |5-9| i dont know how to simplify the last... (answered by Fombitz)

Method of Substitution 4. Solve by substitution. Check your answers. a) x+2y=3... (answered by solver91311)

I need to change these problems to slope intercept form but i dont know how. 2x-3y=9... (answered by rfer,jim_thompson5910)

i dont know how to add or subtract the expression like this; (2x+x-2)+(-3x+4x+8) and... (answered by elima)