SOLUTION: Hello, I came across this problem and I'm unsure how to solve it: {{{ 5^(2x) * 5^(x+1) = 25 }}} Thank you so much to anyone who helps.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hello, I came across this problem and I'm unsure how to solve it: {{{ 5^(2x) * 5^(x+1) = 25 }}} Thank you so much to anyone who helps.      Log On


   



Question 1016259: Hello,
I came across this problem and I'm unsure how to solve it:
+5%5E%282x%29+%2A+5%5E%28x%2B1%29+=+25+
Thank you so much to anyone who helps.

Found 2 solutions by Edwin McCravy, macston:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
  
+5%5E%282x%29+%2A+5%5E%28x%2B1%29+%22%22=%22%22+25+

Write 25 as a power of 5:

+5%5E%282x%29+%2A+5%5E%28x%2B1%29+%22%22=%22%22+5%5E2+

Add the exponents of 5 on the left

+5%5E%28%282x%29%2B%28x%2B1%29%29+%22%22=%22%22+5%5E2+

The bases are the same positive number other than 1,
therefore the exponents are equal:

+%282x%29%2B%28x%2B1%29+%22%22=%22%22+2+

2x%2Bx%2B1+%22%22=%22%22+2+

3x%2B1%22%22=%22%222

3x%22%22=%22%221

x%22%22=%22%221%2F3 

Edwin

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
+5%5E%282x%29+%2A+5%5E%28x%2B1%29+=+25+
.
5%5E%283x%2B1%29=25
log_base_5%285%5E%283x%2B1%29%29=log_base_5%2825%29
3x%2B1=2
3x=1
x=1%2F3
.
CHECK:
5%5E%282x%295%5E%28x%2B1%29=25
.
5%5E%282%281%2F3%29%295%5E%28%281%2F3%29%2B1%29=25
.
5%5E%282%2F3%295%5E%284%2F3%29=25
.
5%5E%28%282%2F3%29%2B%284%2F3%29%29=25
.
5%5E%286%2F3%29=25
.
5%5E2=25
.
25=25
.