Question

5^X+2 = 10(8^2X-2)

Answer 1

quick question... is it

1. \[5^{x + 2} = 10(8^{2x - 2})\]

Answer 2

or simply

2. \[5^x + 2 = 10(8^{2x} - 2)\]

Answer 3

5^X+2 = 10(82X-2)
5^X+2 = 820X-20
5^X = 820X-20-2
5^X = 820X-22
ln (5^X) = ln 820X- ln 22
X (1.6) = ln 820X - (3.091)
1.6X = ln 820X - 3.091
e^(1.6X + 3.091) = 820X
e^1.6X e^3.091 = 820X

Answer 4

http://www.wolframalpha.com/input/?i=%28e^%281.6X%29%29*%28e^3.091%29+%3D+820X+

Answer 5

@gerryliyana I think there are a few holes in your solution

\[10\times8^{2} \neq820\] just looking at a simple error

Answer 6

ahh i was typo and wrong

Answer 7

I though 82X not 8^2X,

Answer 8

and it's a bit hard to answer the question without the correct version of the equation

Answer 9

If 5^X+2 = 10(8^2X-2), then

5^X+2 = 10(8^2X-2)
5^X+2 = 10*8^2X-20
5^X = 10*8^2X-20 -2
5^X = 10*8^2X-22
ln(5^X) = ln(10*8^2X)- ln(22)
X ln 5 = ln 10 + ln (8^2X) - ln 22
X ln 5 = ln 10 + 2X ln 8 - ln 22
X ln 5 - 2X ln 8 = ln 10 - ln 22
X (ln 5 - 2 ln 8) = ln 10 - ln 22
X = (ln 10 - ln 22)/(ln 5 - 2 ln 8)

Answer 10

\[X = \frac{ \ln 10 - \ln 22 }{ \ln 5 - 2*\ln 8 } \]

Answer 11

X = 0.30926625501