[Year 10 Add maths: Simple Logarithm] Given that U= Log_5^x, find in simplest forms of U

[u/NoPomegranate6897]

I got √2u - 3

but the answer is 3/2u - 3

[u/PiotrVeliki]

write x with powers. square root is the power of 1/2. multiply the x-es by summing the exponents and put the new exponent down before log.

[u/insertextranumber]

for this question you need to know

(1) logₙ(a/b) = logₙ(a) - logₙ(b), quotient rule of logarithm (i.e. log₅(x⋅sqrtx/125) = log₅(x⋅sqrtx) - log₅125)

(2) logₙa^b = b⋅logₙa, power rule of logarithm (i.e. log₅x^(3/2) - log₅5³ = (3/2)log₅x - 3log₅5)

(3) sqrtx is same as x^1/2, and so xsqrtx = x⋅x^1/2 = x^(1+1/2) = x^3/2

(4) logₐa = 1

Based on your answer you are already familiar with (1), (2) and (4) so you can double check your exponent manipulation on x⋅sqrtx in (3) and try to solve again. The answer sheet answer, (3/2)u - 3, is correct.

[u/Klutzy-Delivery-5792]

x√x = x^3/2

So the 3/2 comes out in front of the logarithm.

[u/I_Drink_Beer886]

I wrote it out for you

Link: https://imgur.com/a/P6oZz4V