Question

Solve the following equations.
log3(x^2) = 4

Answer 1

x = 9

Explanation:

given,

log₃ x² = - 4

using logarithmic identity

logₐ x = b

x = aᵇ

log xᵃ = a log x

converting into exponential form as the base is 3

log₃ x² = 4

2 log₃ x = 4

log₃ x = 2

converting

x = 3²

x = 9

Hence, the solution of X will be equal to x = 9

Answer 2

x = 0.125

Explanation:

Given:

log₃(x²) = 1

Now,

From the properties of log

logₓ (z)=
`(\log(z))/(\log(x))` (where the base of the log is equal for both numerator and the denominator)

also,

log(xⁿ) = n × log(x)

thus,

using the above properties, we can deduce the results as:

logₓ(y) = n is equivalent to y = xⁿ

therefore,

the given equation can be deduced as:

log₃(x²) = 1

or

2log₃(x) = 1

or

log₃(x) = 0.5

into,

x = 0.5³

or

x = 0.125