Question

solve for x
if logbaseto10(x²-12x+36)=2​

Answer 1

Required Answer:-

Given:

• $\sf \log_{10}(x^{2}- 12x + 36) = 2$

To find:

• The values of x satisfying the equation.

Answer:

• The values of x satisfying the equation are -4 and 16.

Solution:

Given,

$\sf \log_{10}(x^{2}-12x+36) =2$

➡ 10² = x² - 12x + 36

➡ x² - 12x + 36 - 100 = 0

➡ x² - 12x - 64 = 0

➡ x² - 16x + 4x - 64 = 0

➡ x(x - 16) + 4(x - 16) = 0

➡ (x + 4)(x - 16) = 0

By Zero-Product Rule,

Either (x + 4) = 0 or (x - 16) = 0

So,

➡ x + 4 = 0

➡ x = -4

Also,

➡ x - 16 = 0

➡ x = 16

Hence, the values of x satisfying the equation are -4 and 16.

Learn More:

1. Logarithm of a negative number is undefined.
2. Logarithms to the base 10 are called common logarithms.
3. Logarithms of base e are called natural logarithms.
4. Logarithms are developed to make complicated calculations easier and simpler.

Some Formulas of Logarithms:

1. $\sf log_{x}(1) = 0,x > 1$
2. $\sf log_{x}(x) = 1,x > 1$
3. $\sf log_{a}(xy) = log_{a}(x) + log_{a}(y)$
4. $\sf log_{a}( \frac{x}{y} ) = log_{a}(x) - log_{a}(y)$