Question

Solve 4x − 5 = 6 for x using the change of base formula log base b of y equals log y over log b.

−4.226
−3.708
5.774
6.292

Answer 1

Explanation:

4^x-5 = 6

Apply the ln rule

x^y = z

(y)*ln(x) = z

4^x-5 = 6

(x-5)*ln(4) = ln(6)

x-5 = ln(6)/ln(4)

x-5 = 1.292

x = 6.292

Therefore, the correct answer is the last option.

!!

Answer 2

Option 4 - x=6.292

Explanation:

Given : Expression
`4^(x-5)=6`

To find : Solve the expression using change of base formula?

Solution :

Expression
`4^(x-5)=6`

Change of base formula is
`\log_b y=(\log_a y)/(\log_a b)`

Step 1 - Taking log both side in the expression,

`\log(4^(x-5))=\log (6)`

Apply logarithmic property,
`\log a^x=x\log a`

`(x-5)\log(4)=\log (6)`

Step 2 - Taking log one side,

`x-5=(\log (6))/(\log(4))`

Step 3 - Apply change base formula,

`x-5=\log_4 6`

Step 4 - Solve,

`x=\log_4 6+5`

`x=1.292+5`

`x=6.292`

Therefore, Option 4 is correct.