Question

Which is equivalent to 2^5x = 7?
A. x = log2 (7/5) B. x=(log2 7)/5 C. x = (log7 2)/5 D. x= (log7 5)/2

and how you solved it

Answer 1

Answer:

Rewrite the equation to exponential form

logs 2 (5x + 7) = 5 ⇒ 2 5 = 5x + 7

⇒ 32 = 5x + 7

⇒ 5x = 32 – 7

5x = 25

Divide both sides by 5 to get

x = 5

Example 2

Solve for x in log (5x -11) = 2

Solution

Since the base of this equation is not given, we therefore assume the base of 10.

Now change the write the logarithm in exponential form.

⇒ 102 = 5x – 11

⇒ 100 = 5x -11

111= 5x

111/5 = x

Hence, x = 111/5 is the answer.

Example 3

Solve log 10 (2x + 1) = 3

Solution

Rewrite the equation in exponential form

log10 (2x + 1) = 3n⇒ 2x + 1 = 103

⇒ 2x + 1 = 1000

2x = 999

On dividing both sides by 2, we get;

x = 499.5

Verify your answer by substituting it in the original logarithmic equation;

⇒ log10 (2 x 499.5 + 1) = log10 (1000) = 3 since 103 = 1000

Example 4

Evaluate ln (4x -1) = 3

Solution

Rewrite the equation in exponential form as;

ln (4x -1) = 3 ⇒ 4x – 3 =e3

But as you know, e = 2.718281828

4x – 3 = (2.718281828)3 = 20.085537

x = 5.271384

Example 5

Solve the logarithmic equation log 2 (x +1) – log 2 (x – 4) = 3

Solution

First simplify the logarithms by applying the quotient rule as shown below.

log 2 (x +1) – log 2 (x – 4) = 3 ⇒ log 2 [(x + 1)/ (x – 4)] = 3

Now, rewrite the equation in exponential form

⇒2 3 = [(x + 1)/ (x – 4)]

⇒ 8 = [(x + 1)/ (x – 4)]

Cross multiply the equation

⇒ [(x + 1) = 8(x – 4)]

⇒ x + 1 = 8x -32

7x = 33 …… (Collecting the like terms)

x = 33/7

Example 6

Solve for x if log 4 (x) + log 4 (x -12) = 3

Answer 2

hey mate the value of x is –3/2

hope it helps