How do you solve $7^(x – 2) = 12x$ ?

Question

1764 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-01T14:00:59

A step in the correct direction!! Perhaps someone else can take it further. I used the Iteration method.

$color(red)("Method 1")$
Plot the straight line graph of $12x$
Plot the curve of $7^(x-2)$
The intersections are where the values for $x$ are.

Or try iteration for $x =7^x/588$

$color(red)("Method 2")$
$7^(x-2) -> (7^x)/(7^2)$

so $7^(x-2) = 12x -> 7^x = (7^2)(12)x$

$7^x = 588x$

Taking logs
$x ln(7) = ln(588) + ln(x)$

$x = (ln(588) + ln(x))/(ln(7))$

By iteration

Set seed value as 1
$x ~= 3.988$ to 3 decimal places

I could not find the seed for the lower one which is in the region of
$x ~= 0.0016$ to 5 dp

Graphs of the log method:
Tony B

Tony B

How do you solve 7^(x – 2) = 12x7^(x – 2) = 12x?