Question

find value of x if log2^x+log3^27=0​

Answer 1

Answer:

We know

log(x) ^n = n logx

log2^x + log 3^27 = x log2 + 27 log 3 = 0

x = - 27 log3 / log2

Hope It Helps

Hope It HelpsKindly Mark Me As Brainliest

Hope It HelpsKindly Mark Me As BrainliestFollow Me

Hope It HelpsKindly Mark Me As BrainliestFollow Me Bye

Answer 2

Before solving the problem, let us know some logarithmic formulae :

• log (a × b) = log (a) + log (b) ..... (i)

• log (aᵇ) = b log (a) ..... (ii)

• log (a) = log (b) gives a = b ..... (iii)

• log (1) = 0 ..... (iv)

Easier way to solve for x :

Here, log (2ˣ) + log (3²⁷) = 0

or, x log (2) + 27 log (3) = 0, using (ii)

or, x log (2) = - 27 log (3)

or, x = - 27 log (3) / log (2)

∴ the required solution is

x = - 27 log (3) / log (2).

Another approach :

Now, log (2ˣ) + log (3²⁷) = 0

or, log (2ˣ * 3²⁷) = log (1) using (i) and (iv)

or, 2ˣ * 3²⁷ = 1 using (iii)

or, 2ˣ = 1/(3²⁷)

or, 2ˣ = 3⁻²⁷

Taking log to both sides, we get

log (2ˣ) = log (3⁻²⁷)

x log (2) = - 27 log (3) using (ii)

or, x = - 27 log (3) / log (2) = - 42.8 (approx.)

∴ the required solution is

x = - 27 log (3) / log (2).