i have problem i can't solve and the book is no help.. anyone got osme hints or somehting i could start off doing?
the problem is...
Solve for x: log(x^3)= (log x)^3
Rewrite it as 3 log x = (log x)^3
The use algebra (divide each side by log x) to get
(log x)^2 = 3
log x = (+ or -) sqrt 3
(There are two solutions)
When log x = sqrt 3,
x = e^(sqrt 3) = 5.652...
When log x = -sqrt 3,
x = e^-sqrt3, x = 0.1769...
There are actually 3 solutions, when you divided through by the log x you eliminated one of them. Try x=1 too.
sin 27 degrees = x \ 8
To solve the equation sin(27 degrees) = x / 8, you can use the following steps:
Step 1: Convert 27 degrees to radians. 27 degrees is approximately equal to 0.4712 radians.
Step 2: Rewrite the equation as sin(0.4712) = x / 8.
Step 3: Multiply both sides of the equation by 8 to isolate x. This gives you 8 * sin(0.4712) = x.
Step 4: Calculate sin(0.4712) either using a calculator or by referring to a table of trigonometric values. The value is approximately 0.4578.
Step 5: Multiply 8 by 0.4578 to find the solution for x. The result is approximately 3.6624.
Therefore, the solution to the equation sin(27 degrees) = x / 8 is x ≈ 3.6624.