Question

logxbase 10whole square- log x base 10-6=0 .what is the valuae of x?​

Answer 1

Required Answer:-

Given:

$\rm \big(log_{10}(x) \big)^{2} - log_{10}(x) - 6 = 0$

To find:

• The value of x.

Solution:

Given that,

$\rm \implies \big(log_{10}(x) \big)^{2} - log_{10}(x) - 6 = 0$

Let us assume that,

$\rm y = log_{10}(x)$

Therefore,

$\rm \implies {y}^{2} - y - 6 = 0$

Now, we will solve the quadratic equation.

$\rm \implies {y}^{2} - 3y + 2y - 6 = 0$

$\rm \implies y(y - 3)+ 2(y - 3)= 0$

$\rm \implies (y + 2)(y - 3)= 0$

By zero product rule,

Either y + 2 = 0 or y - 3 = 0

➡ y = -2, 3

So, when y = -2,

$\rm \implies log_{10}(x) = - 2$

$\rm \implies x = {10}^{ - 2}$

$\rm \implies x = \frac{1}{100}$

When y = 3,

$\rm \implies log_{10}(x) = 3$

$\rm \implies x = {10}^{3}$

$\rm \implies x = 1000$

Hence, the possible values of x are 0.01 and 1000

Answer:

• x = 0.01, 1000

Verification:

Let us verify our result.

When x = 1/100,

$\rm \big(log_{10}(x) \big)^{2} - log_{10}(x) - 6$

$\rm \big(log_{10}(0.01) \big)^{2} - log_{10}(0.01) - 6$

$\rm = {( - 2)}^{2} -( - 2) + 6$

$\rm = 4 + 2 - 6$

$\rm = 0$

Hence, 0.01 is a solution.

Again, when x = 1000,

$\rm \big(log_{10}(x) \big)^{2} - log_{10}(x) - 6$

$\rm = \big(log_{10}(1000) \big)^{2} - log_{10}(1000) - 6$

$\rm = {3}^{2} - 3 - 6$

$\rm = 9 - 9$

$\rm = 0$

Hence, 10³ is a solution of the equation.

Hence, our answers are correct. (Verified)

Answer 2

Answer:

HEYA mate here's the answer Mark as brainliest pleaseeeeee follow