Question

if log p is equal to log 20 at base 10 and q is equal to log 25 at base 10 find the value of x in 2log(x+1)=2p +q​

Answer 1

Answer:

2log(x+1)=2log 20+log25

=log(20^2×25)

it gives

(x+1)^2=20^2×25

x+1=20×5

x+1=100

x=99

Answer 2

The value of x is 99.

Given,

p = log₁₀ 20, q = log₁₀ 25 and 2 log(x+1) = 2p + q

To Find,

Value of x.

Solution,

From question we have,

2log(x+1) = 2 log 20 + log 25

We know that m log n = log $n^{m}$

Therefore, log (x+1)² = log (20)² + log 25

log (x+1)² = log 400 + log 25

We also know that log m + log n = log (m*n)

log (x+1)² = log (10000)

Apply exponential both sides we get,

(x+1)² = 10000

x+1 = 100

x = 99

The value of x is 99.

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