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Exponential Eq.

 

2^t+3=7^t-1

 Dec 8, 2015

Best Answer 

 #3
avatar+130561 
+5

OK......I guess we have 

 

2^(t + 3)   = 7^(t - 1)    ????    if so........take the log of both sides

 

log2^(t +3)  = log7^(t - 1)      and we can write

 

(t +3) log2  = (t - 1) log 7     simplify

 

t log2  + 3log2  = tlog7 - log 7

 

3log2 + log7  = tlog7 - t log2

 

3log2 + log 7  = t [ log 7 - log2]       divide both sides by log 7 - log2

 

[3log2 + log 7 ] / [ log7 - log2]  = t  = about 3.2132

 

 

 

cool cool cool

 Dec 8, 2015
 #1
avatar+130561 
+5

Here's a graphical solution :  https://www.desmos.com/calculator/hvjfai7rfa

 

The solution occurs at about t = 0.91

 

 

cool cool cool

 Dec 8, 2015
 #2
avatar
+5

i think u misunderstood...those are raised to the power............it has somethig to do with log brother.

 Dec 8, 2015
 #3
avatar+130561 
+5
Best Answer

OK......I guess we have 

 

2^(t + 3)   = 7^(t - 1)    ????    if so........take the log of both sides

 

log2^(t +3)  = log7^(t - 1)      and we can write

 

(t +3) log2  = (t - 1) log 7     simplify

 

t log2  + 3log2  = tlog7 - log 7

 

3log2 + log7  = tlog7 - t log2

 

3log2 + log 7  = t [ log 7 - log2]       divide both sides by log 7 - log2

 

[3log2 + log 7 ] / [ log7 - log2]  = t  = about 3.2132

 

 

 

cool cool cool

CPhill Dec 8, 2015
 #4
avatar
+5

im confsed & i thnk its wrong :( sigh.

 Dec 9, 2015

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