Solve for x and y: logx/3 = logy/2 and log(xy) = 5 .

Given, ⇒ 2 log x = 3 log y ⇒ 2 log x - 3 log y = 0 .......(i) Given, log (xy) = 5 ⇒ log x + log y = 5 ......(ii) Multiplying (ii) by 2 we get, ⇒ 2 log x + 2 log y = 10 ......(iii) Subtracting (i) from (iii) we get, ⇒ 2 log x + 2 log y - (2 log x - 3 log y) = 10 - 0 ⇒ 2 log x - 2 log x + 2 log y + 3 log y = 10 ⇒ 5 log y = 10 ⇒ log y = 2 ⇒ y = 10 2 = 100. Substituting value of y in (ii) we get, ⇒ log x + log 100 = 5 ⇒ log x + 2 = 5 ⇒ log x = 3 ⇒ x = 10 3 = 1000. Hence, x = 1000 and y = 100.

Solve the following equation for x:
log₆ (x - 2) + log₆ (x + 3) = 1

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Solve the following equation for x:
log (x + 1) + log (x - 1) = log 11 + 2log 3

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If a = 1 + log_x yz, b = 1 + log_y zx and c = 1 + log_z xy, then show that
ab + bc + ca = abc.

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Mathematics

Solve for x and y: logx/3 = logy/2 and log(xy) = 5 .

Logarithms

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Solve the following equation for x:
log₆ (x - 2) + log₆ (x + 3) = 1

Solve the following equation for x:
log (x + 1) + log (x - 1) = log 11 + 2log 3

If a = 1 + log_x yz, b = 1 + log_y zx and c = 1 + log_z xy, then show that
ab + bc + ca = abc.

Mathematics

Solve for x and y: logx/3 = logy/2 and log(xy) = 5 .

Logarithms

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Solve the following equation for x:log6 (x - 2) + log6 (x + 3) = 1

Solve the following equation for x:log (x + 1) + log (x - 1) = log 11 + 2log 3

If a = 1 + logx yz, b = 1 + logy zx and c = 1 + logz xy, then show thatab + bc + ca = abc.

Solve the following equation for x:
log₆ (x - 2) + log₆ (x + 3) = 1

Solve the following equation for x:
log (x + 1) + log (x - 1) = log 11 + 2log 3

If a = 1 + log_x yz, b = 1 + log_y zx and c = 1 + log_z xy, then show that
ab + bc + ca = abc.