logarithmic problem

[torpid zenith]

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[urban cape]

@warped sphinx start by noticing that the given equation is equivalent to : b^5=a, no bases are given sadly. Try to change b^5 to b^8 such as to get log(8) on one side after taking logarithm on both sides WITHOUT breaking the equation

ehh why'd you do that

that's very not like what I told you to do.

[warped sphinx]

Yeah actually I'm doing like that and I didn't get how to do like u

[urban cape]

brother do you know what a logarithm means

$\log_{b}(a)=c$

[manic hatch]

instantaneousCoffey

[urban cape]

Means that $b^c=a$

[manic hatch]

instantaneousCoffey

[urban cape]

now

[warped sphinx]

Yes ik that

[urban cape]

$b^d = a^{\frac{d}{c}}$

[manic hatch]

instantaneousCoffey

[urban cape]

wait there's an even easier way!

$\log 5=a$

[manic hatch]

instantaneousCoffey

[urban cape]

$\log 5^k=ak$

[manic hatch]

instantaneousCoffey

[urban cape]

@warped sphinx now when is 5^k = 8

[ocean pagoda]

log 5 = a
⁵log 10 = 1/a
⁵log(2×5) = 1/a
⁵log 2 + ⁵log 5 = 1/a
⁵log 2 + 1 = 1/a
⁵log 2 = (1/a)-1
⁵log 2 = (1-a)/a
²log 5 = a/(1-a)

1/log 8
= ⁸log 10
= log(2³, 10)
= (1/3) ²log 10
= (1/3) ²log(2×5)
= (1/3)(²log 2 + ²log 5)
= (1/3)(1 + ²log 5)
= (1/3)(1 + (a/(1-a)))
= (1/3)(1/(1-a))
= 1/(3(1-a))
= 1/(3-3a) -> (b)

[warped sphinx]

Thank youu so much for your help ^_^

[fleet pewter]

@warped sphinx has given 1 rep to @ocean pagoda