Putting aside the uncertainty of what the original equation actually is, how did you go from the first equation to the second? The 11.56 in the second equation happens to be 3.42, but the second equation should not involve x.steveandy2002 said:I need to find x from (3.4)^2x+3=8.5
what i have done is as follows
3.4^2x = 11.56
3.4^2x+3 = 14.56
8.5 - 14.56 = x
x=-6.06
huntoon said:if it is :
3.4(2x+3)=8.5
take the log of both sides...
steveandy2002 said:so based on useing logs would the folllowing be correct??
3.4^(2x+3)=8.5
2x+3log3.4=log8.5
2x=3-log8.5/log3.4
x= 3-log8.5/log3.4/2
x=1.947942814?
The equation above is incorrect. It should besteveandy2002 said:so based on useing logs would the folllowing be correct??
3.4^(2x+3)=8.5
2x+3log3.4=log8.5
This is wrong as well.steveandy2002 said:2x=3-log8.5/log3.4
steveandy2002 said:x= 3-log8.5/log3.4/2
x=1.947942814?
The first step is to isolate the term with the variable, in this case 3.4^2x, by subtracting 3 from both sides of the equation. This will give us 3.4^2x=5.5.
To get rid of the exponent, we can take the logarithm of both sides of the equation. Specifically, we can take the logarithm with base 3.4 because it is the base of the exponent. This will give us log3.4(3.4^2x)=log3.4(5.5).
After taking the logarithm, we can use the logarithm property logb(bx)=x to simplify the left side of the equation to just 2x. This will give us 2x=log3.4(5.5). Finally, we can solve for x by dividing both sides by 2, giving us x=log3.4(5.5)/2.
Yes, the value of x can be negative. In fact, when solving exponential equations with logarithms, it is common to get negative values for the variable.
To check your answer, you can plug it back into the original equation and see if it satisfies the equation. In this case, we can plug in x=log3.4(5.5)/2 and simplify to see if both sides of the equation are equal.