10e^(3x-7)= 5
So what I've done is rewritten it as:
(3x-7)ln10e = ln5
Now I'm a little lost as to what to do next...
Find the value of in10 and in5
multiply the value of in10 wit the varables in the brackets
collect the like terms i.e live the varable with the x term on the left hand side and the others on the right
then solve for x from there.
Goodluck
Your start was incorrect...
the exponent does not apply to the 10, only to the base of e
so ...
e^(3x-7) = 5/10= .5
now take ln of both sides
(3x-7) ln e = ln .5 , but ln e = 1
3x-7 = ln .5
3x = 7 + ln .5
x = (7 + ln .5)/3 , and it is button-pushing time
To solve the equation 10e^(3x-7) = 5, you correctly rewrote it as (3x-7)ln10e = ln5. However, there is a mistake in your rewriting.
The natural logarithm (ln) is based on the number "e." In the expression 10e^(3x-7), the base is already "e," so there is no need to apply the natural logarithm to it.
To solve the equation correctly, we can proceed as follows:
Step 1: Divide both sides of the equation by 10 to isolate the exponential term:
e^(3x-7) = 5/10
e^(3x-7) = 1/2
Step 2: Take the natural logarithm of both sides of the equation to remove the exponential term:
ln(e^(3x-7)) = ln(1/2)
(3x-7)ln(e) = ln(1/2)
Step 3: Simplify the natural logarithm of "e" to 1:
(3x-7) = ln(1/2)
Step 4: Solve for x by isolating the variable:
3x - 7 = ln(1/2)
3x = ln(1/2) + 7
x = (ln(1/2) + 7)/3
Thus, the solution to the equation 10e^(3x-7) = 5 is x = (ln(1/2) + 7)/3.