Question

Solve the exponential equations.
(a) 25^(x+1)+5^(2x)=26
(b) 3(3^x)-3^(x-1)=216

Answer 1

\[5^{2(x+1)}+5^{2x}=25+1\]
\[5^{2(x+1)}+5^{2x}=5^2+5^0\]

so looking at both sides
both sides would be the same if x=0

Answer 2

so x=0 is a solution to the first one

Answer 3

So that's just something you have to eyeball?

Answer 4

A similar approach\[25*25^x+25^x=26\]\[25^x(25+1)=26\]\[25^x=1\]\[x=0\]

Answer 5

ohhhh, clever

Answer 6

you can use what mandolino did to other question

Answer 7

\[3(3^x)-3^x3^{-1}=216=>3^x(3-3^{-1})=216\]

Answer 8

The solution of (a) is x=1
(b) is x=4
I KNOW THE ANSWERS BUT I DON'T KNOW HOW TO DO IT.

Answer 9

\[3*3^x-3^x/3=216\]\[3^x(3-1/3)=216\]\[3^x(8/3)=216\]\[3^x=81\]\[3^x=3^4\]\[x=4\]

Answer 10

\[3^x(3-\frac{1}{3})=216=> 3^{x}(\frac{9-1}{3})=216=> 3^x=216 \cdot \frac{3}{9-1}\]

\[3^{x}=216 \cdot \frac{3}{8}=>3^{x}=27(3)=>3^x=3^33=>3^x=3^4=>x=4\]

Answer 11

Same same

Answer 12

tissue the answer to a is x=0

Answer 13

I' m sorry that I typed the QUESTION (a) wrongly.
(a) should be 25^(x-1)+5^(2x)=26
AND THE ANSWER IS x=1

Answer 14

Do you need to see the solution, or are the example enough?

Answer 15

The example is ENOUGH. THX:)

Answer 16

Actually this is earlier than your typo equation (a)!
\[25^x(1/25+1)=26\]\[25^x(26/25)=26\]\[25^x=26(25/26)\]\[25^x=25^1\]\[x=1\]

Answer 17

it is very kind of you to help me.THANK YOU SO MUCH!

Answer 18

I wrote "earlier" I meant "easier"!! I must be getting sleepy!

Answer 19

25^(x-1)+5^(2x)=26 AND THE ANSWER IS x=1

Answer 20

5^2(x-1) +5^2x=5^2 +5^0
2(x-1)=2 and 2x=0 power coefficients
x-1=1
x=2 ans and 2x=0 x=0 ans