can someone solve 2^3x=5^x+2?

take log both sides
3xlog2 = (x+2)log5
0.903x = 0.699x + 1.398 --->x = 6.853

Due to lack of brackets, question may be read in many different ways. Unfortunately there is only ONE correct way.

Could it be :-
(2^3) x = (5^x) + 2
OR
2^(3x) = 5^(x + 2)
OR
2^(3x) = (5^x) + 2
OR could it be something else.?

Suppose you learn nothing else this year, understand that brackets MUST be used.
Failure to do so means that people are only GUESSING what the question could be .
This then leads to time being wasted by many.

From the answerers given, it is clear that people are only guessing as to how the question is meant to read.

Not good enough I`m afraid.

2^(3x) = 5^(x+2) ?

--> (2³)^x = 5² · 5^x --> 8^x = 25· 5^x --> (8/5)^x = 25 -->
x= log_(8/5) 25 = log 25 / log (8/5) = log 25/ (log8-log5) -->

x= 2·log5 / (3·log2 - log5) = 2·log5 / [ 3·log(10/5) - log5]

x= 2·log5 / ( 3log10- 3·log5-log5)

x= 2·log5 / (3- 4·log5)

Saludos

Is the (x+2) the exponent?
And is 3x the exponent or just the 3?


I'll suppose (x+2) is the exponent, and so is 3x



3x log2 = (x+2)log 5
because log (a^b)=b loga
and (3x)=(x+2)log5/log2 after dividing both sides by log 2
let log5/log2=c
Then 3x=cx+2c
and x(3-c)=2c
and x=(2c)/(3-c)
c=log5/log2=2.3219280949
x=6.8486





EDIT: given what Teddy boy took the notation to mean, he has the wrong answer. It's shouldn't agree. Only x was the exponent here (and in the 1st step) log(5^x + 2)
but was treated as one in the next.
HmgGuy was wrong to not take the log of the entire right side.
Kim's is diffetrent in the 2nd decimal place because of rounding to 3 places.



l

2^(3x) = 5^(x + 2)
log_2[2^(3x)] = log_2[5^(x + 2)]
(3x)log_2(2) = (x + 2)log_2(5)
3x = (x + 2)log_2(5)
3x = xlog_2(5) + 2log_2(5)
3x - xlog_2(5) = log_2(5^2)
x[3 - log_2(5)] = log_2(25)
x = log_2(25)/[3 - log_2(5)]

3xlog(2) = xlog 5 + 2

3x log2 - x log 5 = 2

x (3 log 2 - log 5) = 2

x = 2 / (3 log2 - log5)

2^3x=5^x+2
log(2^3x) = log(5^x + 2)
3xlog 2 = (x + 2)log 5
3xlog 2 = xlog 5 + 2log 5
3xlog 2 - xlog 5 = 2log 5
x(3log 2 - log 5) = 2log5
x = (2log5)/(3log 2 - log 5)
x = 6.8486 answer

Hope this helps.

teddy boy

2^3x=5^x+2
3xIn2 = xIn5 + In2
x(3In2 - In5) = In2
x = In2/3In2 -In5