The solutions of function y = 253ˣ is 3.55
What are the properties of logarithms?
There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
According to the problem, we will use some of the basic logarithmic properties,
Given as function :y=253ˣ
Substitute y = 1170 in given function
1170=253ˣ
253ˣ=1170
3ˣ = 1170/25
3ˣ = 243/5
Take natural logarithms both sides
log₁₀3ˣ = log₁₀(243/5)
log₁₀3ˣ = log₁₀243 -log₁₀5
log₁₀3ˣ = log₁₀3⁵ -log₁₀5
xlog₁₀3 = 5log₁₀3 -log₁₀5
log₁₀5 = 5log₁₀3 - xlog₁₀3
log₁₀5 = (5 - x)log₁₀3
0.70 = (5 - x)0.48
0.70/0.48 = 5 - x
1.45 = 5 - x
x = 5 - 1.45
x = 3.55
Hence, the solutions of function y = 25*3ˣ is 3.55
Learn more logarithmic properties here:
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