Question

Solve and round answer to nearest hundredth please.

Answer 1

Answer:

Step-by-step explanation:

Solve this by using natural logs.  Taking the natural log of both sides:

$ln(7*16^{8x-8})=ln(3)$

To undo the multiplication, we use addition:

$ln(7)+ln(16)^{8x-8}=ln(3)$

The rule says we can now bring the exponent down in front of the ln:

$ln(7)+(8x-8)ln(16)=ln(3)$

Now we will subtract ln(7) from both sides:

(8x - 8)ln(16) = ln(3) - ln(7)

Now we will divide both sides by ln(16):

$8x-8=\frac{ln(3)-ln(7)}{ln(16)}$ then add 8 to both sides:

$8x=\frac{ln(3)-ln(7)}{ln(16)}+8$ which simplifies to

8x = 7.694401895 so

x = .9618002368 or, rounded,

x = .96

(Rest assured I did the math and checked the answer and it checked out perfectly!)  I recommend you learn the laws of natural and common logs cuz they're kinda important!! :)