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Logarithms

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Logarithms

1 2 3 4			最近活動

Find x if log₁₀[log₂(log₃9)] = x Maths Platter	0	0	4d

Find log₃₀8 if log₃₀3 = x and log₃₀5 = y Maths Platter	0	0	4d

Find k if log₂x / 4 = log₂y / 6 = log₂z / 3k and x³y²z = 1 Maths Platter	0	0	4d

Find a if logₐ5 + logₐ25 + logₐ125 + logₐ625 = 10 Maths Platter	0	0	4d

If aˣ = bʸ = cᶻ = dʷ (a ≠ 1) then prove that logₐabcd = x (1/x + 1/y + 1/z + 1/w) Maths Platter	0	0	4d

If a = log₂₄12, b = log₃₆24, c = log₄₈36, then prove that 1 + abc = 2bc Maths Platter	0	0	4d

If log₁₅x + log₁₅(x + 2) = 1, then provide that x = 3 Maths Platter	0	0	4d

Simplify logₐ81 + logₐ9 - 5logₐ3 Maths Platter	0	0	5d

Simplify logₓx + logₓx³ + logₓx⁵ + ..... + logₓx²ⁿ⁻¹ Maths Platter	0	0	5d

Simplify log₁₀15 + log₁₀8 - log₁₀12 Maths Platter	0	0	5d

Simplify log (x²/yz) + log (y²/zx) + log (z²/xy) Maths Platter	0	0	5d

Simplify 3 log 7 + log 49 - log 343 - log 7 Maths Platter	0	0	5d

Solve log x = log 3 + 3 log 2 - 2 log 4 Maths Platter	0	0	5d

Solve log x / log 4 = log 625 / log 25 Maths Platter	0	0	5d

Solve log x / log 9 = log 729 / log 81 Maths Platter	0	0	5d

Solve log₁₀x + log₁₀(x - 3) = 1 Maths Platter	0	0	5d

If ( log x)/1 = ( log y)/2 = ( log z)/5 then show that x^(4)y^(3)z^(-2) = 1 Maths Platter	0	0	5d

If ( log x)/(b+c-2a) = ( log y)/(c+a-2b) = ( log z)/(a+b-2c) then show xyz = 1 Maths Platter	0	0	5d

Prove 2^(- log_(2) 8) = 1/8 Maths Platter	0	0	5d

Prove 5^(3 log_(5) root()(2)) = 2 root()(2) Maths Platter	0	0	5d

Prove log₀.₅8 = -3 Maths Platter	0	0	5d

Prove log₀.₂₅4 = -1 Maths Platter	0	0	5d

Show that log_(y) x^(2) log_(z) y^(4) log_(x) z^(6)=48 Maths Platter	0	0	5d

Show that log_(y) x^(2) log_(z) y^(2) log_(x) z^(2 )= 8 Maths Platter	0	0	5d

Show that log_(y) x log_(z) y log_(z) z = 1 Maths Platter	0	0	5d

Show that log_(y) x^(2) log_(z) y^(5) log_(x) z^(4 )= 40 Maths Platter	0	0	5d

Prove xyz + 1 = 2yz if x = log₂ₐa, y = log₃ₐ2a, z = log₄ₐ3a Maths Platter	0	0	5d

Prove x log_() b/a = log_() a if a³⁻ˣb⁵ˣ = aˣ⁺⁵b³ˣ Maths Platter	0	0	5d

Prove x = 10^( 1/(1- log_(10) z) ) if y = 10^( 1/(1- log_(10) x) ) and z = 10^( 1/(1- log_(10) (y)) ) Maths Platter	0	0	5d

Prove that a^( log_(a^(2)) x)b^( log_(b^(2)) y)c^( log_(c^(2)) z) = root()(xyz) Maths Platter	0	0	5d

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Logarithms

Find x if log₁₀[log₂(log₃9)] = x

Find log₃₀8 if log₃₀3 = x and log₃₀5 = y

Find k if log₂x / 4 = log₂y / 6 = log₂z / 3k and x³y²z = 1

Find a if logₐ5 + logₐ25 + logₐ125 + logₐ625 = 10

If aˣ = bʸ = cᶻ = dʷ (a ≠ 1) then prove that logₐabcd = x (1/x + 1/y + 1/z + 1/w)

If a = log₂₄12, b = log₃₆24, c = log₄₈36, then prove that 1 + abc = 2bc

If log₁₅x + log₁₅(x + 2) = 1, then provide that x = 3

Simplify logₐ81 + logₐ9 - 5logₐ3

Simplify logₓx + logₓx³ + logₓx⁵ + ..... + logₓx²ⁿ⁻¹

Simplify log₁₀15 + log₁₀8 - log₁₀12

Simplify log (x²/yz) + log (y²/zx) + log (z²/xy)

Simplify 3 log 7 + log 49 - log 343 - log 7

Solve log x = log 3 + 3 log 2 - 2 log 4

Solve log x / log 4 = log 625 / log 25

Solve log x / log 9 = log 729 / log 81

Solve log₁₀x + log₁₀(x - 3) = 1

If ( log x)/1 = ( log y)/2 = ( log z)/5 then show that x^(4)y^(3)z^(-2) = 1

If ( log x)/(b+c-2a) = ( log y)/(c+a-2b) = ( log z)/(a+b-2c) then show xyz = 1

Prove 2^(- log_(2) 8) = 1/8

Prove 5^(3 log_(5) root()(2)) = 2 root()(2)

Prove log₀.₅8 = -3

Prove log₀.₂₅4 = -1

Show that log_(y) x^(2) log_(z) y^(4) log_(x) z^(6)=48

Show that log_(y) x^(2) log_(z) y^(2) log_(x) z^(2 )= 8

Show that log_(y) x log_(z) y log_(z) z = 1

Show that log_(y) x^(2) log_(z) y^(5) log_(x) z^(4 )= 40

Prove xyz + 1 = 2yz if x = log₂ₐa, y = log₃ₐ2a, z = log₄ₐ3a

Prove x log_() b/a = log_() a if a³⁻ˣb⁵ˣ = aˣ⁺⁵b³ˣ

Prove x = 10^( 1/(1- log_(10) z) ) if y = 10^( 1/(1- log_(10) x) ) and z = 10^( 1/(1- log_(10) (y)) )

Prove that a^( log_(a^(2)) x)b^( log_(b^(2)) y)c^( log_(c^(2)) z) = root()(xyz)

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