If log 10 to base 8 = X, evaluate log 5 to base 8 in...

If log 10 to base 8 = X, evaluate log 5 to base 8 in terms of X.
  • A. \(\frac{1}{2}\)X
  • B. X-\(\frac{1}{4}\)
  • C. X-\(\frac{1}{3}\)
  • D. X-\(\frac{1}{2}\)
Correct Answer: Option C
Explanation
\(log_810\) = X = \(log_8{2 x 5}\)

\(log_82\) + \(log_85\) = X
Base 8 can be written as \(2^3\)
\(log_82 = y\)
therefore \(2 = 8^y\)
\(y = \frac{1}{3}\)

\(\frac{1}{3} = log_82\)

taking \(\frac{1}{3}\) to the other side of the original equation

\(log_85 = X-\frac{1}{3}\)

explanation courtesy of Oluteyu and Ifechuks

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Contributions (91)

cotterell
4 years ago
If log10 to base 8 = X

I.e log5 - base8

Log(5 - 8)

X = log3

Applying the law of indices which if 3^0 = 1, a = 1

So log3 = 1

Applying the rule of zero power law

Log3^-1 = 1/3 I.e X=log1/3
Shozlee
5 years ago
Woahhhhhh ! All cool..............



Log 10 base 8 = X



log 5 base 8 = log 10/2



" law of log



log 10 base 8 - log 2 base 8



since log 10 is 'X' lets equate log 2 base 8 to 'Y'



log 2 base 8 = Y



2^1 = 8^y ==== 2^1 = 2^3y



equating the powers



1=3y ===== y = 1/3



recall X - Y



log 5 base 8 = X-(1/3)
Tahywoh
5 years ago
Hmm,my people,let's just think. If we simplify log 5 base8 log 2 base 8,we will get log 10 base 8 and we have been given that log 10 base 8 = X. Now let's move on.

Log 5 base 8 log 2 base 8 = X. Are u with me?,,we must be careful here. Can you still remember the rule that says loga^2 base a^3 gives 2/3 log a base a which is eaqual to 2/3 X 1 = 2/3.

Can you still undstd. Go along with me my brother and sisster,

so let's apply d same thing here, log 2 ^1 base 8. Do not forget that 8 can also be written as 2^3.

You got it? If u are with me,am sure u're undstding a lilltle bit.

So we have log 2^1 base 2 ^3 to be 1/3 log 2 base 2 which will now give us 1/ 3 X 1 = 1/3.

U understand me,don't relax pls,keep going along with me.

Recall that we say log5 base 8 X log 2 base 8 = X.

Now that we know our log 2 base 8 = 1/3,so we put into d equation to have..

Log 5 base 8 1/ 3 = X.

Therefore,log 5 base 8 = X - 1/3.
MUHAMMED SODIQ
6 years ago
since log5 to base 8 = x, and x = log10 to base 8

i.e log5 to base 8 =log10 to base8

then x =log5 to base 8 - log10 to base 8, 5/10=1/2,i.e 2^-1 and 8=2^3,= -1/3=x
Log8 10=X is given.

Log8 5 = log8(10/2).

Then log10 - log2 = X - log2.

(-log8 2 =X) 8(x) =2

2^(3y) = 2^(1)

Eliminate 2, e.g (2^((3x)) =2^(1)) Then you are left with 3x =1.

= 3x =1

x=1/3

.∴ x=-1/3

By bringing down the - negative sign. The answer is x=-(1/3)
peterpan20
2 years ago
we are told that we should calculate the distance of the foot of the ladder from the wall. firstly is that we go back to our question that says a ladder 6m long, which mean that our ladder is 6m long and leans against a vertical wall.we all know a vertical line is either a standing line or a slanting line but in this question we are actually given that it is a vertical wall .so to solve this question we are given 60° with the wall ,which mean that the angle will be inbetween the hypoth and adjacent or the angle will be facing the opposite side of the triangle .now our hypo is 6m long will our opposite side of the angle is not given but we can call it "x" sintheta=opposite/hypo

opposite=x,hypoth=6,theta=60 or √3/2

sin 60°=x/6 or √3/2=x/6 so when you cross multiply, it

will be x=6√3/2 ,so 2 divided by 6 will give us 3 therefore the answer is 3√3 .
Smallking
3 years ago
Brilliantly done, keep it up
Ezichi
9 months ago
that answer is wromg
fidel91
3 years ago
pls,were z d 2 coming from,d 2 z confusing me o
Ben Godwin
3 years ago
for your jamb CBT test question and answer contact Mr Jackson on 09052169005. for your help and how to go about answering it
pharteemarh
6 years ago
pls we nid an undastandable nd simple solution.
sunday felicia
3 years ago
WOW!!! U ARE GUYZ ARE WONDERFUL NOE I GOT IT
it can also be done this way

log10 to base 8 is the same as log5x2 base 8

therefore log5+log2=x,

so, log2 to base 8 is the same as log 2 to base 2 raise to the power of 3

then, 1/3log2 to base 2 will be 1/3

since lo5 to base 3 is x, then x+1/3 will be x=-1/3.
Felix Brown
6 years ago
Log8 raise to power 10 minus log8 raise to power 5 equal to X gives log8 raise to power 2 equal to X. Therefore, 8 raise to power x = 2 raise to power one. Then, 2 raise to power 3x= 2 raise to power one . Then, 2 cancel on both sides wht will b left is 3x=1. X=1\3 when X crosses equality sign ,d ansa will b X-1\3. Tanx nd God bless una
sammy6829
4 years ago
very wrong sis.

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