Question

log(base a) 4 + log(base a) 16 + log(base a) 64 + log(base a)256 = 10 Then a =?

Answer 1

Answer:

a is 4

pls see the ans in pic

as log a +log b = log(ab)

we can see the ans

Answer 2

The value of a = 4

Given :

$\displaystyle \sf{ log_{a} \:4 + log_{a} \:16 + log_{a} \:64 +log_{a} \:256 = 10 }$

To find :

The value of a

Solution :

Step 1 of 2 :

Write down the given equation

The given equation is

$\displaystyle \sf{ log_{a} \:4 + log_{a} \:16 + log_{a} \:64 +log_{a} \:256 = 10 }$

Step 2 of 2 :

Find the value of a

$\displaystyle \sf{ log_{a} \:4 + log_{a} \:16 + log_{a} \:64 +log_{a} \:256 = 10 }$

$\displaystyle \sf{ \implies log_{a} \:(4 \times 16 \times 64 \times 256) = 10 }$

$\displaystyle \sf{ \implies log_{a} \:( {4}^{1} \times {4}^{2} \times {4}^{3} \times {4}^{4} ) = 10 }$

$\displaystyle \sf{ \implies log_{a} \:( {4}^{1 + 2 + 3 + 4} ) = 10 }$

$\displaystyle \sf{ \implies log_{a} \:( {4}^{10} ) = 10 }$

$\displaystyle \sf{ \implies 10 \: log_{a} \:4 = 10 }$

$\displaystyle \sf{ \implies log_{a} \:4 = 1 }$

$\displaystyle \sf{ \implies log_{a} \:4 = log_{4} \: 4 }$

$\displaystyle \sf{ \implies a = 4 }$

Hence the required value of a = 4

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If 2log((x+y)/(4))=log x+log y then find the value of (x)/(y)+(y)/(x)

https://brainly.in/question/24081206

2. If log (0.0007392)=-3.1313 , then find log(73.92)

https://brainly.in/question/21121422