Question

Solve the following exponential equation.

36= 3^x+5 + 3^x+4

Answer 1

\[36= 3^{x+5} + 3^{x+4}\]
Divide everything by 3:
\[12= {x+5} + {x+4}\]
Combine like terms:
\[12= 2x+9\]
Solve for x:
\[3= 2x\]
\[1.5=x\]

Answer 2

I think x = -2

Answer 3

HI :D

Answer 4

Hi...here's why...itll take a minute

Answer 5

Yeah, x does =-2

Thanks anyways @Urebaa

Answer 6

\[36 = 3^{4+x} + 3^{ 5+x}\]
\[y = 3^{x; }; 3^{x+4}+3^{x+5}\]
\[324 *3^{x} = 324
y = 36\]
\[324y = 36
y = 19
3^{x = 1/9
3^{2+x}}=1\]
\[3^{2+x}= 3^{0}
2+x = 0
x=-2\]

Answer 7

\[36= 3^{x}\times3^{5} + 3^{x}\times3^{4}\]
\[36 = 3^{x} (3^{5} + 3^{4} + 1)\]
\[36 = 3^{x} {325)\]

That's how i"ve been doing it so far

Answer 8

The way i input got a little messed up.. sorry

Answer 9

LOL yeah care to explain ?

Answer 10

I'm confused as to what you're doing in your solution...

Answer 11

Let me retype again...this time correctly.

Answer 12

Sounds good. thanks :)

Answer 13

Starting on the 3rd line...the first 2 were OK
\[324 * 3^{x}=324\]
\[y=36\]
\[324y = 36\]
\[y = 1/9\]
\[3^{x}= 1/9\]
\[3^{2+x}= 1\]
\[3^{2+x}= 3^{0}\]
2+x = 0
x = -2

Answer 14

do it this way split the 1st power of 3

\[36 = 3 \times 3^{x + 4} + 3^{x + 4}\]

so then factoring you get

\[36 = 3^{x + 4}( 3 + 1)\]

or

\[36 = 3^{x +4}(4)\]

divide both sides by 4

\[9 = 3^{x + 4}\]

now rewrite 9 interms of a power of 3

\[3^2 = 3^{x + 4}\]

equate the powers and solve for x

2 = x + 4

Answer 15

hope it makes sense...

Answer 16

and remember some of the basics for indices

\[3^1 \times 3^{x +4} = 3^{1 + x + 4} = 3^{x + 5}\]

when multiplying, add the powers

Answer 17

I am still confused LOL

out of what I wrong above, what am I doing wrong?

Answer 18

I don't understand how either of you are solving the problem.

Answer 19

wrote *

Answer 20

well you correctly showed that the terms can be split to show that

\[36 = 3^x \times 3^5 + 3^x \times 3^4 \]

you error is in factoring

the correct factorisation is

\[36 = 3^x(3^5 + 3^4)\]

there is now + 1

so then the next step is division

\[\frac{36}{3^5 + 3^4} = 3^x\]

or

\[\frac{36}{243 + 81} = 3^x\]

which becomes

\[\frac{36}{324} = 3^x\]

simplifying and you get

\[\frac{1}{9} = 3^x\]

now write your fraction as a power of 3

\[3^{-2} = 3^x\]

hence your answer.

taking a larger common factor

\[3^{x + 4}....instead .. of ... 3^x\]

would have reduced the amount of work needed for the solution.

so the error was early in your solution, ad was caused by an incorrect factorisation or an expression

Answer 21

oops should be

there is no + 1

Answer 22

WAIT , i get it. Thank you @campbell_st , your method explains it :) thanks for taking the time to explain it :)

Answer 23

glad to help.... your method does work with a little more care with factoring

Answer 24

https://www.mathway.com
this site doesn't help explaining it but it does give the answers lol @lovethecreation

Answer 25

Thanks @tswavy :)