solve the equation?.........?

=====> e^8x=7/4
8x ln e=ln 7/4=0.5596
x=0.069951973
God bless you

Qu 1

e^(8x) = 7/4

8x = ln (7/4)

x = (1/8) ln (7/4)

Qu 2

Will ASSUME that you mean :-

10^(4 - 3x) = 5-------( but of course should not have to assume anything in a subject such as maths !)

4 - 3 x = log 5-------------logs to base 10

3x = 4 - log 5

x = ( 4 - log 5 ) / 3

PS

AS GIVEN question MUST actually be read as :-

( 10^4 ) - 3x = 5

3x = 10^4 - 5

x = 9995 / 3

1)
4e^(8x) = 7
e^(8x) = 7/4
8x = ln(7/4)
x = [ln(7/4)]/8

2)
10^(4 - 3x) = 5
4 - 3x = log(5)
3x = 4 - log(5)
x = [4 - log(5)]/3

You need to know your log laws to do these two questions. I suggest you go and revise them. Here are the solutions:

4e^8x = 7
e^8x = 7/4
ln e^8x = ln (7/4)
8xln(e) = ln (7/4) Note ln(e) = 1
8x = ln (7/4)
x = 1/8 ln (7/4)
Wack that in your calculator for a numerical approximation.

For the next one, instead of using natural log ( log to base e, which is "ln" on your calculator ), we use log to base 10, written with a "log" on your calculator.

10^4-3x = 5
log 10^4-3x = log 5
(4-3x)log 10 = log 5 (Note log 10 = 1)
4-3x = log 5
3x = 4 - log5
x = 1/3(4 - log 5)

Hope that helps.

(10 x 10 x 10 x 10) - 5
X = ___________________
3

X = 9995 / 3

4e^(8x) = 7
=> ln4 + 8x = ln7
=> x = (1/8) (ln7 - ln4) = 0.06995

10^(4-3x) = 5
=> (4-3x) ln10 = ln5
=> 4 - 3x = ln5 / ln10 = 0.6990
=> 3x = 4 - 0.699 = 0.301
=> x = 0.301/3 = 0.1003.